{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## RBF Kernel Principal Component Analysis"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Implementation of RBF Kernel Principal Component Analysis for non-linear dimensionality reduction"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "> from mlxtend.feature_extraction import RBFKernelPCA"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Overview"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Most machine learning algorithms have been developed and statistically validated for linearly separable data. Popular examples are linear classifiers like Support Vector Machines (SVMs) or the (standard) Principal Component Analysis (PCA) for dimensionality reduction. However, most real world data requires nonlinear methods in order to perform tasks that involve the analysis and discovery of patterns successfully.\n",
    "\n",
    "The focus of this overview is to briefly introduce the idea of kernel methods and to implement a Gaussian radius basis function (RBF) kernel that is used to perform nonlinear dimensionality reduction via BF kernel principal component analysis (kPCA)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Principal Component Analysis\n",
    "\n",
    "The main purpose of principal component analysis (PCA) is the analysis of data to identify patterns that represent the data “well.” The principal components can be understood as new axes of the dataset that maximize the variance along those axes (the eigenvectors of the covariance matrix). In other words, PCA aims to find the axes with maximum variances along which the data is most spread.\n",
    "\n",
    "![](./RBFKernelPCA_files/pca_1.png)\n",
    "\n",
    "For more details, please see the related article on [`mlxtend.feature_extraction.PrincipalComponentAnalysis`](./PrincipalComponentAnalysis.md)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Nonlinear dimensionality reduction\n",
    "\n",
    "The “classic” PCA approach described above is a linear projection technique that works well if the data is linearly separable. However, in the case of linearly inseparable data, a nonlinear technique is required if the task is to reduce the dimensionality of a dataset.\n",
    "\n",
    "![](./RBFKernelPCA_files/linear_vs_nonlinear.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Kernel functions and the kernel trick\n",
    "\n",
    "\n",
    "\n",
    "The basic idea to deal with linearly inseparable data is to project it onto a higher dimensional space where it becomes linearly separable. Let us call this nonlinear mapping function $\\phi$ so that the mapping of a sample $\\mathbf{x}$ can be written as $\\mathbf{x} \\rightarrow \\phi (\\mathbf{x})$, which is called \"kernel function.\"\n",
    "\n",
    "Now, the term \"kernel\" describes a function that calculates the dot product of the images of the samples $\\mathbf{x}$ under $\\phi$.\n",
    "\n",
    "$$\\kappa(\\mathbf{x_i, x_j}) =  \\phi (\\mathbf{x_i}) \\phi (\\mathbf{x_j})^T$$\n",
    "\n",
    "More details about the derivation of this equation are provided in this excellent review article by Quan Wang: [Kernel Principal Component Analysis and its Applications in Face Recognition and Active Shape Models](http://arxiv.org/abs/1207.3538).[[1](#References)]\n",
    "\n",
    "In other words, the function $\\phi$ maps the original d-dimensional features into a larger, k-dimensional feature space by creating nononlinear combinations of the original features. For example, if $\\mathbf{x}$ consists of 2 features:\n",
    "\n",
    "$$\n",
    "\\mathbf{x} = \\big[x_1 \\quad x_2\\big]^T \\quad \\quad \\mathbf{x} \\in I\\!R^d\n",
    "$$\n",
    "\n",
    "$$\n",
    "\\Downarrow \\phi\n",
    "$$\n",
    "\n",
    "$$\n",
    "\\mathbf{x}' = \\big[x_1 \\quad x_2 \\quad x_1 x_2 \\quad x_{1}^2 \\quad x_1 x_{2}^3 \\quad \\dots \\big]^T \\quad \\quad \\mathbf{x} \\in I\\!R^k (k >> d)\n",
    "$$\n",
    "\n",
    "\n",
    "Often, the mathematical definition of the RBF kernel is written and implemented as\n",
    "\n",
    "$$\n",
    "\\kappa(\\mathbf{x_i, x_j}) = exp\\bigg(- \\gamma \\; \\lVert\\mathbf{x_i - x_j }\\rVert^{2}_{2} \\bigg)\n",
    "$$\n",
    "\n",
    "where $\\textstyle\\gamma = \\tfrac{1}{2\\sigma^2}$ is a free parameter that is to be optimized.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Gaussian radial basis function (RBF) Kernel PCA\n",
    "\n",
    "\n",
    "\n",
    "In the linear PCA approach, we are interested in the principal components that maximize the variance in the dataset. This is done by extracting the eigenvectors (principle components) that correspond to the largest eigenvalues based on the covariance matrix:\n",
    "\n",
    "$$\\text{Cov} = \\frac{1}{N} \\sum_{i=1}^{N} \\mathbf{x_i} \\mathbf{x_i}^T$$\n",
    "\n",
    "Bernhard Scholkopf ([Kernel Principal Component Analysis](http://dl.acm.org/citation.cfm?id=299113) [[2](#References)]) generalized this approach for data that was mapped onto the higher dimensional space via a kernel function:\n",
    "\n",
    "$$\\text{Cov} = \\frac{1}{N} \\sum_{i=1}^{N} \\phi(\\mathbf{x_i}) \\phi(\\mathbf{x_i})^T$$\n",
    "\n",
    "However, in practice the the covariance matrix in the higher dimensional space is not calculated explicitly (kernel trick). Therefore, the implementation of RBF kernel PCA does not yield the principal component axes (in contrast to the standard PCA), but the obtained eigenvectors can be understood as projections of the data onto the principal components.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### RBF kernel PCA step-by-step\n",
    "\n",
    "\n",
    "#### 1. Computation of the kernel (similarity) matrix.\n",
    "\n",
    "In this first step, we need to calculate\n",
    "\n",
    "$$\\kappa(\\mathbf{x_i, x_j}) = exp\\bigg(- \\gamma \\; \\lVert\\mathbf{x_i - x_j }\\rVert^{2}_{2} \\bigg)$$\n",
    "\n",
    "for every pair of points. E.g., if we have a dataset of 100 samples, this step would result in a symmetric 100x100 kernel matrix.\n",
    "\n",
    "#### 2. Eigendecomposition of the kernel matrix.\n",
    "\n",
    "Since it is not guaranteed that the kernel matrix is centered, we can apply the following equation to do so:\n",
    "\n",
    "$$K' = K - \\mathbf{1_N} K - K \\mathbf{1_N} + \\mathbf{1_N} K \\mathbf{1_N}$$\n",
    "\n",
    "where $\\mathbf{1_N}$ is (like the kernel matrix) a $N\\times N$ matrix with all values equal to $\\frac{1}{N}$. [[3](#References)]\n",
    "\n",
    "Now, we have to obtain the eigenvectors of the centered kernel matrix that correspond to the largest eigenvalues. Those eigenvectors are the data points already projected onto the respective principal components.\n",
    "    "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Projecting new data\n",
    "\n",
    "So far, so good, in the sections above, we have been projecting an dataset onto a new feature subspace. However, in a real application, we are usually interested in mapping new data points onto the same new feature subspace (e.g., if are working with a training and a test dataset in pattern classification tasks).\n",
    "\n",
    "Remember, when we computed the eigenvectors $\\mathbf{\\alpha}$ of the centered kernel matrix, those values were actually already the projected datapoints onto the principal component axis $\\mathbf{g}$.\n",
    "\n",
    "If we want to project a new data point $\\mathbf{x}$ onto this principal component axis, we'd need to compute $\\phi(\\mathbf{x})^T  \\mathbf{g}$.\n",
    "\n",
    "Fortunately, also here, we don't have to compute $\\phi(\\mathbf{x})^T  \\mathbf{g}$ explicitely but use the kernel trick to calculate the RBF kernel between the new data point and every data point $j$ in the training dataset:\n",
    "\n",
    "$$\\phi(\\mathbf{x})^T  \\mathbf{g}  = \\sum_j \\alpha_{i} \\; \\phi(\\mathbf{x}) \\; \\phi(\\mathbf{x_j})^T$$\n",
    "\n",
    "$$=  \\sum_j \\alpha_{i} \\; \\kappa(\\mathbf{x}, \\mathbf{x_j})$$\n",
    "\n",
    "\n",
    "and the eigenvectors $\\alpha$ and eigenvalues $\\lambda$ of the Kernel matrix $\\mathbf{K}$ satisfy the equation\n",
    "$\\mathbf{K} \\alpha = \\lambda \\alpha$, we just need to normalize the eigenvector by the corresponding eigenvalue."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### References\n",
    "\n",
    "\n",
    "[1] Q. Wang. [Kernel principal component analysis and its applications in face recognition and active shape models](http://arxiv.org/abs/1207.3538). CoRR, abs/1207.3538, 2012.\n",
    "\n",
    "[2] B. Scholkopf, A. Smola, and K.-R. Muller. [Kernel principal component analysis](http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.128.7613). pages 583–588, 1997.\n",
    "\n",
    "[3] B. Scholkopf, A. Smola, and K.-R. Muller. [Nonlinear component analysis as a kernel eigenvalue problem](http://www.mitpressjournals.org/doi/abs/10.1162/089976698300017467#.VBh9QkuCFHg). Neural computation, 10(5):1299–1319, 1998."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example 1 - Half-moon shapes"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We will start with a simple example of 2 half-moon shapes generated by the `make_moons` function from scikit-learn."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAiwAAAFyCAYAAADWG4HzAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nVZ4JiyRJqjwTFkmSVHn/F1yWVVRptSPfAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x105ff4f98>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "from sklearn.datasets import make_moons\n",
    "\n",
    "X, y = make_moons(n_samples=50, random_state=1)\n",
    "\n",
    "plt.scatter(X[y==0, 0], X[y==0, 1], \n",
    "            color='red', marker='o', alpha=0.5)\n",
    "plt.scatter(X[y==1, 0], X[y==1, 1], \n",
    "            color='blue', marker='^', alpha=0.5)\n",
    "plt.ylabel('y coordinate')\n",
    "plt.xlabel('x coordinate')\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Since the two half-moon shapes are linearly inseparable, we expect that the “classic” PCA will fail to give us a “good” representation of the data in 1D space. Let us use `PCA` class to perform the dimensionality reduction."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAiwAAAF5CAYAAAC83HEwAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nKj0TFkmSVHomLJIkqfT+P0HL867G7JwNAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10c95e080>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from mlxtend.feature_extraction import PrincipalComponentAnalysis as PCA\n",
    "\n",
    "pca = PCA(n_components=2)\n",
    "X_pca = pca.fit(X).transform(X)\n",
    "\n",
    "plt.scatter(X_pca[y==0, 0], X_pca[y==0, 1], \n",
    "            color='red', marker='o', alpha=0.5)\n",
    "plt.scatter(X_pca[y==1, 0], X_pca[y==1, 1], \n",
    "            color='blue', marker='^', alpha=0.5)\n",
    "\n",
    "plt.xlabel('PC1')\n",
    "plt.ylabel('PC2')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As we can see, the resulting principal components do not yield a subspace where the data is linearly separated well. Note that PCA is a unsupervised method and does not “consider” class labels in order to maximize the variance in contrast to Linear Discriminant Analysis. Here, the colors blue and red are just added for visualization purposes to indicate the degree of separation."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next, we will perform dimensionality reduction via RBF kernel PCA on our half-moon data. The choice of $\\gamma$\n",
    "depends on the dataset and can be obtained via hyperparameter tuning techniques like Grid Search. Hyperparameter tuning is a broad topic itself, and here I will just use a $\\gamma$-value that I found to produce “good” results."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "from mlxtend.data import iris_data\n",
    "from mlxtend.preprocessing import standardize\n",
    "from mlxtend.feature_extraction import RBFKernelPCA as KPCA\n",
    "\n",
    "kpca = KPCA(gamma=15.0, n_components=2)\n",
    "kpca.fit(X)\n",
    "X_kpca = kpca.X_projected_"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Please note that the components of kernel methods such as RBF kernel PCA already represent the projected data points (in contrast to PCA, where the component axis are the \"top k\" eigenvectors thar are used to contruct a projection matrix, which is then used to transform the training samples). Thus, the projected training set is available after fitting via the `.X_projected_` attribute."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAiwAAAGHCAYAAACTRAlZAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nAdaHiEZgbQIWAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10dff1978>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(X_kpca[y==0, 0], X_kpca[y==0, 1], \n",
    "            color='red', marker='o', alpha=0.5)\n",
    "plt.scatter(X_kpca[y==1, 0], X_kpca[y==1, 1], \n",
    "            color='blue', marker='^', alpha=0.5)\n",
    "\n",
    "plt.title('First 2 principal components after RBF Kernel PCA')\n",
    "plt.xlabel('PC1')\n",
    "plt.ylabel('PC2')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The new feature space is linearly separable now. Since we are often interested in dimensionality reduction, let's have a look at the first component only."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAgAAAAGHCAYAAADGJeoHAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x105b8eb70>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "\n",
    "plt.scatter(X_kpca[y==0, 0], np.zeros((25, 1)), \n",
    "            color='red', marker='o', alpha=0.5)\n",
    "plt.scatter(X_kpca[y==1, 0], np.zeros((25, 1)), \n",
    "            color='blue', marker='^', alpha=0.5)\n",
    "\n",
    "plt.title('First principal component after RBF Kernel PCA')\n",
    "plt.xlabel('PC1')\n",
    "plt.yticks([])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can clearly see that the projection via RBF kernel PCA yielded a subspace where the classes are separated well. Such a subspace can then be used as input for generalized linear classification models, e.g.,  logistic regression."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Projecting new data"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Finally, via the transform method, we can project new data onto the new component axes."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAhcAAAFkCAYAAACThxm6AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\nAAAPYQAAD2EBqD+naQAAIABJREFUeJzs3Xl4k1Xa+PHvk6VL0n2lCC2lYMFRUMoiYBURF5ARREVB\nHZDBYUZHHVBH0dEXGVHGmRF+4oXb6PiKDiovvurLuOICxUGUtgrILktpgUJ32nRJm+f3x2nSpAsU\nSJq0vT/X9VxpTp48OQ2luXvOfe6j6bqOEEIIIYS3GPzdASGEEEJ0LRJcCCGEEMKrJLgQQgghhFdJ\ncCGEEEIIr5LgQgghhBBeJcGFEEIIIbxKggshhBBCeJUEF0IIIYTwKgkuhBBCCOFVElwIIYQQwqt8\nHlxomna3pmn7NU2r1jTtW03Thp3k3NGapm3QNK1I0zSbpmk7NE37g6/7KIQQQgjvMfny4pqm3Qz8\nHfgN8B0wF/hU07RzdV0vauUpVcAyYEvj15cAL2uaVqnr+j982VchhBBCeIfmy43LNE37Ftik6/p9\njfc14BDwnK7rz7TzGquBSl3XZ/iso0IIIYTwGp9Ni2iaZgYygC+cbbqKZNYCI9t5jYsaz/3aB10U\nQgghhA/4clokDjAChc3aC4H0kz1R07RDQHzj8xfouv7Pk5wbC1wNHABqzqK/QgghRHcTAvQBPtV1\nvdhbF/VpzsVZuAQIAy4G/qJp2l5d199p49yrgbc6rGdCCCFE13Mr8C9vXcyXwUUR0AAkNmtPBI6e\n7Im6rh9s/PInTdN6AAuAtoKLAwBvvvkmAwcOPNO+dktz585lyZIl/u5GpyLv2ZmR9+30yXt2ZuR9\nOz07duzgtttug8bPUm/xWXCh67pd07Rs4ArgQ3AldF4BPHcalzICwSd5vAZg4MCBDBky5Ax72z1F\nRkbKe3aa5D07M/K+nT55z86MvG9nzKtpBb6eFnkWeL0xyHAuRbUArwNomvY00NO5EkTTtLuAPGBn\n4/MvA+4Hlvq4n0IIIYTwEp8GF7quv6tpWhywEDUd8gNwta7rxxtP6QH0dnuKAXgalVxSD/wMPKjr\n+su+7KcQQgghvMfnCZ26ri8Hlrfx2B3N7j8PPO/rPgkhhBDCd2RvkW5s2rRp/u5CpyPv2ZmR9+30\nyXt2ZuR9Cww+rdDZETRNGwJkZ2dnSxKPEEIIcRpycnLIyMgAyNB1Pcdb1w3UOhdCCCHaIS8vj6Ki\n1rZqEkKJi4sjOTm5Q19TggshhOik8vLyGDhwIDabzd9dEQHMYrGwY8eODg0wJLgQQohOqqioCJvN\nJkUERZucRbKKiookuBBCCNF+UkRQBBpZLSKEEEIIr5LgQgghhBBeJcGFEEIIIbxKggshhBBCeJUE\nF0IIIQLS5s2bGT16NGFhYRiNRrZs2cKCBQswGLz/0bVu3ToMBgPr16/3+rW7IwkuhBBCBJz6+npu\nvPFGSktLWbp0KStWrCAlJQVN01oEF08//TQffPDBWb+mpmln9LyPP/6YJ5544qxfvyuR4EIIIUTA\n+fnnn8nLy+PBBx9k9uzZTJ8+ncjISB577LEWRcOeeuoprwQXZ+qjjz5i4cKFfnv9QCTBhRBCiJZs\nNigshNpav7x8YWEhAJGRkR7tBoOBoKAgf3SpTZ19jy5fkOBCCCFEk9pa+J//gYcegocfhkcegU8/\nhYaGDuvCHXfcwZgxY9A0jRtvvBGDwcDYsWMBWuRcGAwGbDYbr7/+OgaDAYPBwKxZs056/YKCAiZP\nnkxYWBiJiYnMmzeP2traFkHChg0bmDp1KikpKYSEhJCcnMy8efOoqanx6Ovy5ctdfTEYDBiNRtfj\nf/vb3xg9ejRxcXFYLBaGDh3K6tWrz/o9CnRSoVMIIbo6mw2ys+HAAbBYYPBgSEuD1nIM3n4bPvwQ\noqMhKgqKi+G111RwMWFCh3T3t7/9Lb169WLRokXcd999DBs2jMTEREDlRbjnRrz55pv8+te/ZsSI\nEfzmN78BIC0trc1r19TUMHbsWPLz87nvvvtISkpixYoVfPnlly1yLlatWkV1dTV33XUXsbGxfPfd\ndyxbtoyCggLeeecdV18PHz7M2rVreeutt1oEKM899xyTJk3itttuo66ujrfffpupU6eyZs0axo8f\n75X3KxBJcCGEEF1ZWRk8/zz8+CM4HKDr8O9/w7RpcOWVnucWFkJWFiQmQkKCaouMhIMH4fPP4fLL\nITTU8zknTsAXX8DGjVBXB0OHwrhx6hpnaMSIEdTU1LBo0SIyMzOZMmVKm+dOnz6dOXPm0LdvX6ZP\nn37Ka7/00kvs3buXVatWua575513MmjQoBbnPvPMMwQHB7vuz549m7S0NB599FHy8/Pp1asXI0aM\n4Nxzz2Xt2rVMmzatxTX27NnjcY3f//73XHTRRTz77LNdOriQaREhhOjKPv1UjVr06wcXXKAOgFWr\n4OhRz3MLC6GiAmJjPdtjY6GkRI1iuKuthRdegDfeUNeqqFBTKs8+C8eP++57Ogsff/wxSUlJHgFL\nSEiIa9TDnXtQYLPZKC4uZuTIkTgcDnJzc9v1eu7XKCsro7S0lMzMTHJycs7iuwh8ElwIIURX5XDA\nt9+qKQ7nh5ymQe/eKlDYvt3z/IgINTJx4oRn+4kTqj083LM9Nxc2b4b+/SE1VV33/PNh9241AhKA\nDh48SL9+/Vq0p6ent2g7dOgQM2fOJDY2lrCwMOLj4125IOXl5e16vTVr1jBy5EhCQ0OJiYkhISGB\nF154od3P76xkWkQIIbqyhgZoq+iUw+F5PyUFBg2CDRvUc8LDobQUjh2D669XUyTuDhxQ13efKjEa\nISwMfvoJTjKdEegcDgfjxo2jrKyM+fPnk56ejtVqpaCggBkzZuBo/t61Iisri0mTJjFmzBheeOEF\nkpKSMJvNvPbaa6xcubIDvgv/keBCCCG6KoMBMjLg/fchKUl98IMKFiIi1IiDO02DmTNV0LFli8q1\niIiAq6+GG25oef2QkKY8DvdkyLo6FWB0kNMpfpWSksJPP/3Uon3nzp0e97du3cqePXtYsWIFt956\nq6t97dq17X799957j9DQUD799FNMpqaP21dffbXd/e2sJLgQQoiu7Kqr1PTHtm1gtao8CbMZJk2C\n5OSW58fGwv33w/79Khk0Pl5Nd7T2ATpokJpyyc+HXr1UW0mJuh0+3HffUzNWq5WysrJ2nTthwgQ+\n//xzVq9ezQ2NAZPNZuOVV17xOM+5nLT5CMXSpUtbBBNWqxWAiooKIiIiPK6haRr19fWu4OLAgQN+\nLfjVUSS4EEKIriwpCR58UE117NyppjqGDVOrOtr6i99gUEtVTyU1FW65RSWHbtum2qxWGD8eRozw\n3vdwChkZGaxdu5YlS5bQs2dPUlNTGd5GcHPnnXfy/PPPc/vtt7N582bXUlRngOA0YMAA0tLSuP/+\n+8nPzyciIoLVq1e3GsRkZGSg6zr33HMPV199NUajkZtvvplrr72WZ599lquvvprp06dTWFjI8uXL\n6d+/P1u2bPHJexEoJLgQQoiuLi4OJk/2/nU1TY2M/OIXanSkvl6tSunXr+3A5bQu3/o1mrc/++yz\nzJkzh8cee4zq6mpmzJjRZnARGhrKl19+yT333MPzzz+PxWLhtttu45prruGaa65xnWcymVizZg33\n3nsvixcvJiQkhClTpnD33XczePBgj2tOmTKFe++9l7fffttV6+Lmm2/m8ssv57XXXmPx4sXMnTuX\n1NRUnnnmGfbv39/lgwuts5ct1TRtCJCdnZ3NkCFD/N0dIYToMDk5OWRkZCC//0RbTvUz4nwcyNB1\n3WvrY2UpqhBCCCG8SoILIYQQQniVBBdCCCGE8CoJLoQQQgjhVRJcCCGEEMKrJLgQQgghhFdJcCGE\nEEIIr5LgQgghhBBeJcGFEEIIIbxKggshhBBCeJUEF0IIIYTwKgkuhBBCBKTNmzczevRowsLCMBqN\nbNmyhQULFmAweP+ja926dRgMBtavX+/1a3dHElwIIYQIOPX19dx4442UlpaydOlSVqxYQUpKCpqm\ntQgunn76aT744IOzfs22dmE9lY8//pgnnnjirF+/K5HgQgghRMD5+eefycvL48EHH2T27NlMnz6d\nyMhIHnvsMWw2m8e5Tz31lFeCizP10UcfsXDhQr+9fiCS4EIIIUTAKSwsBCAyMtKj3WAwEBQU5I8u\ntUnXdX93IeBIcCGEEKKF48fhzTehqqrjX/uOO+5gzJgxaJrGjTfeiMFgYOzYsQAtci4MBgM2m43X\nX38dg8GAwWBg1qxZJ71+QUEBkydPJiwsjMTERObNm0dtbW2LIGHDhg1MnTqVlJQUQkJCSE5OZt68\nedTU1Hj0dfny5a6+GAwGjEaj6/G//e1vjB49mri4OCwWC0OHDmX16tVn/R4FOpOvX0DTtLuBB4Ae\nwI/APbquf9/GudcDvwMuBIKBn4AFuq5/5ut+CiFEV1dQAHFxEBx86nPXroX/+z9ITIQrr/R939z9\n9re/pVevXixatIj77ruPYcOGkZiYCKi8CPfciDfffJNf//rXjBgxgt/85jcApKWltXntmpoaxo4d\nS35+Pvfddx9JSUmsWLGCL7/8skXOxapVq6iuruauu+4iNjaW7777jmXLllFQUMA777zj6uvhw4dZ\nu3Ytb731VosA5bnnnmPSpEncdttt1NXV8fbbbzN16lTWrFnD+PHjvfJ+BSRd1312ADcDNcCvgAHA\nS0AJENfG+UtQgUgGkAYsAmqBwSd5jSGAnp2drQshRHeSnZ2tt/f3X0mJrs+bp+urVp36ukeO6Pqd\nd+r6hAm6fv/9ul5Zeern7Nun6zk57eh0O3399de6pmn66tWrPdoXLFigGwwGj7awsDD9jjvuaNd1\nly5dqhsMBo/rVldX6/3799cNBoO+bt06V3tNTU2L5y9evFg3Go36oUOHXG2///3vW/SprWvU19fr\nF1xwgT5u3Lh29fdsnepnxPk4MET34ue/r6dF5gIv6br+hq7rO4HfAjag1TErXdfn6rr+N13Xs3Vd\n/1nX9UeBPcAvfdxPIYTo0tatg5074YsvoKjo5Od+9ZWaFhk8GA4cgP/85+Tn19erKZTXXoPSUq91\n2Sc+/vhjkpKSmDJliqstJCTENerhLthtiMdms1FcXMzIkSNxOBzk5ua26/Xcr1FWVkZpaSmZmZnk\n5OScxXcR+HwWXGiaZkaNQHzhbNN1XQfWAiPbeQ0NCEeNdgghhDgDpaVqmiMxEY4eha+/bvvco0dV\ncJGYCEFBYLXCp5+ePPciJwd++gkOHYJALxNx8OBB+vXr16I9PT29RduhQ4eYOXMmsbGxhIWFER8f\n78oFKS8vb9frrVmzhpEjRxIaGkpMTAwJCQm88MIL7X5+Z+XLnIs4wAgUNmsvBFr+K7buQcAKvOvF\nfonOwn4CdIf6ut7ta7sNzBb1dVEBnKiDqCiIjgVzuGrXDE1fC9HNrVsHhw/DL34BRqMavRgzRuVf\nNOcctRg0SN3v1Qt27VKjF63lXtTXq+BD0yA2Fj7/HC69FKKjffot+ZzD4WDcuHGUlZUxf/580tPT\nsVqtFBQUMGPGDBwOxymvkZWVxaRJkxgzZgwvvPACSUlJmM1mXnvtNVauXNkB34X/+Dyh80xpmjYd\neAy4Ttf1Uwziwdy5c1ssWZo2bRrTpk3zUQ+FTxQegJISiAgB9oO9Ehy1ULkPcIDDDrXFoEXAjh1Q\n+DPYNDCHQK8UGD4RLOFgDoOoIWCySKAhurWSEjVqEROjAoukJNi6VY1e3Hij57nHjqngorZW/fdy\nOnFCBRCXXAKhoZ7PcY5aJCerRNFt29ToxaRJPv/WXE6n+FVKSgo//fRTi/adO3d63N+6dSt79uxh\nxYoV3Hrrra72tWvXtvv133vvPUJDQ/n0008xmZo+bl999dV299ebVq5c2SKo8dUIii+DiyKgAUhs\n1p4IHD3ZEzVNuwV4GbhR1/Wv2vNiS5YsYciQIWfST+Fv9hNQXQX/+w5s/xjsFRASCumx8IsUsPYA\nRx0YQtWIhTEMcn6A7QcgLBysFqirgt3bgRAYlAqWJLBXga6rQCO6MdAACTZEt7J+PeTlQVoaVFaq\nNqu19dELkwlGj4a6upbXsVrV6IQ791ELS+N/r5iYjh+9sFqtlJWVtevcCRMm8Pnnn7N69WpuuOEG\nQOVTvPLKKx7nOZeTNh+hWLp0aYtgwmq1AlBRUUFERITHNTRNo76+3hVcHDhwwG8Fv1r7gzsnJ4eM\njAyvv5bPggtd1+2apmUDVwAfgiuH4grgubaep2naNOAfwM26rn/iq/4JP3NOedTboCwHPv83bP4e\n4o0QrsGJKthWCOgwJBLC+kJdY+qNsRcc+ACs4RCcCuYiMAdBnRXy9sL554M1FWz5YDsEIUlQX6Wu\nBTKqIbqVH39UH/IlbplrRqOKu3ft8gwuYmJgxoz2XzsnR41UGI0qgAFwOGD//o4dvcjIyGDt2rUs\nWbKEnj17kpqayvDhw1s998477+T555/n9ttvZ/Pmza6lqM4AwWnAgAGkpaVx//33k5+fT0REBKtX\nr241iMnIyEDXde655x6uvvpqjEYjN998M9deey3PPvssV199NdOnT6ewsJDly5fTv39/tmzZ4pP3\nIlD4elrkWeD1xiDjO9TqEQvwOoCmaU8DPXVdn9F4f3rjY/cC32ua5hz1qNZ1vcLHfRUdpd4GpTkq\nwAAo3Ar5/4H4UAgPA3SIbAB7GOwphPQySBgNJY1/dtVaocaufmM2hINeAmhg6gn2LVBjBEtPqC0C\nDBDWGGjUV6k2SxKUl6ux3uiekHpF06iGEF3M3LlNIxbN9ehxdteurYXUVBWouEtMBLc6U2esremG\n5u3PPvssc+bM4bHHHqO6upoZM2a0GVyEhoby5Zdfcs899/D8889jsVi47bbbuOaaa7jmmmtc55lM\nJtasWcO9997L4sWLCQkJYcqUKdx9990MHjzY45pTpkzh3nvv5e2333bVurj55pu5/PLLee2111i8\neDFz584lNTWVZ555hv3793f54ELTfVy2VNO0u4A/oqZDfkAV0drc+Ng/gRRd18c23v8KuLSVy/y3\nruutLl/VNG0IkJ2dnS3TIp2Bc8SibBtU7ofQJMjbBR++BNERQAJQD0GlUH4OlB2AyVdCv0ugrnGN\nW7URVrwABgOEJYKhVrWXVENQCdz4KzhnGJTvVM+JHgy2AjjxM+gmyC2AbT+roESPh0Hj4frrIdQq\noxiiU/k2J4eRGRnI7z/RFue0R1s/I27TIhm6rnttfazPEzp1XV8OLG/jsTua3b/c1/0RfuQ+YmGv\nhMq9UF0Apnqw6qrN0BeMJ6DeCrYTYI6EHsNVEmfkeeo6+nY4d4zKPOt9FAy91Z9m9kIYcCXEJqvz\ng6PBmgy1JRCaCOU/wQ+H4IcfISYILCYotcGmN4DdMH4yxAyTUQzRKdQC2/zdCSHaIHuLCN+zn4C6\ncrXSAxPUlkFwPISeA2gQGgTn9IeiBigrhlojFAZDVSEMHA0po8GSrAIFa7L6evKv4fIbodoCB06o\n24yrYfLv1XVri9Vt1PlgNKvXbgiHPQchLBaiTKAngrUPhMfB7h+gvEqdV1euDue0jRABpBZVifAE\n0LUrJYjOLGCXooouot4GB76G0sMQHg6hhqYRC2MQNNjBoMPIycAO2P0t5DWAMQFGnK+CiKBoiM0A\nY4i6pvPrGXfBsUlQblOZaFFW1V4XqkZBrMnquaHnQPl20HvBCR0Sw8HRAA0hoDkgthoqi6BoJ1jc\nMsPN4TKSIQJKLbAJFVzUAj/7tztCtEmCC+E7Fcfgf1fD1o+B46BFq5UcQ1OgLg+iLwS9EBw1ED8I\npk2EvI1gT4CE1KZgAZpum3+dcI5K03DXPBixJqtgI6QHGFZDdTmYY8HggHoT1NjAYIX4X0BwlEr8\ntBWAOappJANkZYnwi1rUmn5QQUUpENR4tGP/MSH8QoIL4Rv1NvjfJbDpa4gNg2gD2Epg28fAABh8\nLhiC1MoNc2TTKEPqWM/g4Uy5X8M92LjwCsh6B04EQ3wdVB6GSjsMHQYRFtDrVW5GbTEYzGB3W3Ym\nIxmig7mPVIDaBXIbEAqEAO0vHSVEx5LgQnif/QQUF8HWnyDWAtYktTIjvBLQYP8hGDJeFcaKPA8i\n0lsfofAm53Wn3gGY4ZvvIa8E4mph6HVw1dVQewSsvdSUiTlSLWF1shWAJUoCC9GhGlCBhXOUwowK\nLMyoQMO3a/2EOHMSXAjvcq4IydsJehFEa2A4rHIbTJUqebPAAPQBS7AasfBVQNGa0FCYcSdMnALH\n9oP5GCQ37qNXVKRGLCxJ6r6jDtAbC3A1QFCUTJEIn2s+DVKDCiYMqNGKINSmTfXItIgIXBJcCO8y\nWVSuQlgIEA+lJyAW0I3QYAZbg0qs7DnYM6eio8XGqqOhpqkPzsRP55LX8l1QXwaVeRCaAGVbVXtF\nBVTr0OtSSOjtn/6LLsk5DXKkHCIjm5abhgIRgHMvTztq1OIcv/RSiFOT4EJ4h/sOpkFREGaBQWnw\n7UYw62A1Q2kwFNbByCvUB3sgcA9unImf1mR1v7pAlRzXgIiB0BCkNmTYtRGKTaCvUxsxTJ3acjcn\nIc5AA7DjIHzxb7huPCSlqsDChBrBADV6UQFUIzkXInBJcCHOXvNy3gDVR+AXZmAAHPwJSsrB1h9G\nXgNTb/NbV0+q+SqT0HNUrkVIkmr77EvYuBbirBDfB8pq4d//A9hg+m0yTSLOiPs0SJUOm36Avfvg\nu29hah8I0tQoRR3gQI1eVDfel584EagkuBBnzzkVUlOi9vQAMARDzTEYOQIyLlG/DXuPgR5p/uzp\nqbU2koEDig7A1mzoXQ+hRjVdEgFE1MOO9+FAL9mjRJy25qtBdufB5loIzoBNlZBxAEJSm0YqTqBG\nLgxADCr/QohAJMGFODvO6RBzlFrGWVuiPmD1BvUXv8EI5wz1XBHSWThHMhqq4eAuqDsBpkhwhEJD\n4w6KwWYo26f+5JTAQpwm99UgQTps/w6ohNhEOFoFmzfBtD5QrUElMBq18yOopM6f/NJrIU5Nggtx\n5ppPh1QfhZpCCIlTKyxih4PR0vErQrzJGKKOuP5qK/gSq1peqzWAboaaYggNhrjkppUkIKtJxEk5\np0KclTbNqG3K9+6C2AGABuGxsH077DsAPVPVyhALTcGFCEx9+vRh7NixvPbaa/7uil9JcCHOXPPp\nEENw0+hFSCLEDgVjaOcNLNydMwjOHQUf/QD1dRBTA+UNYNwH6Rmg5cPx/KbzpeCWaIP7VIizKFaI\nDt8cgOOx0MMIdTpoFjUNsj4Xru8DVk2NVojA1tY28ady5MgRXn75Za6//noGDRrk5V51PNm4TJwd\nazKYglVNiOAYtVLEUQPRg9S0QlcILEB9LzfcDxNuUpukHSsGamFABoy4XG3E5jwa6lTQJYGFaIX7\nVEg4ajWIvQzKjoEpBOq2gp4L+hY45wAYv4Fzj8IIpK5FV3b48GGeeOIJfvjhB393xStk5EKcOfsJ\nwABVQNH3ENsPtHqwpqndSLuasGiYMQMmToRD34DxKCQOhPoTKrgyWaDmuMo3MUfJNIlwOVlhrCBU\n8dexV0BlAwyoU0tM7RoMq4ZIM/Tp0UHLTh31UHu8aVm5O80IIQnqZ1l4na53rXqr8lMizky9DY5s\nhJUL4PW/wcf/hHefgP/8GwwRaoqkq4qNhfMyIfEXKogKPUdNBdXXQEm2yj0p3wrHs5qO0hz1nolu\nxzkNsr7x+AY1FfIDsIPGapsaWOIhvAfEJEOPZEjvDQPPhdRUOMORdkXXVUn71o7mGmqgbDsUfQsl\nm5uOom/hxC4VOHeQBQsWYDAY+Pnnn5k5cybR0dFERUUxa9YsampqWpz/5ptvMnToUCwWC7GxsUyb\nNo38/KapymXLlmEymaioqHC1/f3vf8dgMPDAAw+42hwOB+Hh4cyfP/+UfXzyySfp3bs3VquVK664\ngu3bt7c4p7S0lAceeIBBgwYRHh5OZGQkEyZMYMuWLa5z1q1bx/Dhw9E0jZkzZ2IwGDAajbzxxhsA\nbNiwgalTp5KSkkJISAjJycnMmzev1fchUMjIhTgzJgt8tQm+3wihPSHGCo6j8NNeYC/06+JTAs1r\nYlQXQEOVGrEwR6jpESfZl6Rba2t/EFPjY+c3PlaDyrFwrggx4qVpkNJcqCtt2a6ZVDXaELefVXMY\nhPZQo3GWXqpN16EqD0J7q8383DnsUF/Z+usaQsB05sXlnLkLU6dOpW/fvixevJicnBz+8Y9/kJiY\nyNNPP+06d9GiRTz++OPccsst3HnnnRw/fpznnnuOyy67jNzcXCIiIsjMzETXdTZs2MCECRMA9aFt\nNBrJyspyXSs3NxebzcZll1120v499thjLFq0iIkTJzJ+/HhycnK46qqrsNvtHuft27ePDz/8kJtu\nuonU1FQKCwt56aWXGDNmDNu3b6dHjx4MHDiQhQsX8vjjjzNnzhwyMzMBGDVqFACrVq2iurqau+66\ni9jYWL777juWLVtGQUEB77zzzhm/x74kwYU4fc6NyTZvh8hwiAgFLRhCosEWBZv2wsTiwKnC6SvO\nwCIouql0ePQgz2mSepuaSHdW/RTdVjCqRgWoYMK9MBaoaY8QfLAixBQBJ/Z6BhH1VWp0sbWA19IL\nbIfUOSarSggJimyqYeOu+giUb1PTKR40CE9rKqV/FjIyMnj55Zdd94uKinj11VddwUVeXh4LFizg\nqaee4qGHHnKdN2XKFC688EKWL1/Oww8/zODBgwkPDycrK8sjuLjhhht47733sNlsWCwW1q9fj8Fg\ncH2wt6aoqIi//vWv/PKXv+SDDz5wtf/pT3/iqaee8jh30KBB7N6926Pt9ttvJz09nVdffZVHH32U\nhIQExo8fz+OPP87IkSOZPn26x/nPPPMMwcFNoebs2bNJS0vj0UcfJT8/n169erX37ewwMi0iTo9r\nY7LPwHgYInQIzQNzCRjqwNwDyuxQUuLvnnYsazJYkj2nSQCqCtQvdwwqB8N5uFczFV1OLWq0wnnU\nokYm6miWiyxnAAAgAElEQVTagMxOU2GsE42POUcsvMrSE4JiGuvRRIApXCUdW1NU8NBcUCRYequf\nYV2HugqwpraenB0cC5pZXSe0hzqCYhofi295/mnSNI05c+Z4tGVmZlJcXExlpRoxWb16Nbquc9NN\nN1FcXOw6EhIS6N+/P1999ZXrWqNGjWL9+vUAbN++nZKSEh5++GEcDgcbN24EVMBx/vnnExER0Wa/\n1q5di91u55577vFo/8Mf/tDiXLO5abTH4XBQUlKCxWIhPT2dnJycdr0P7oGFzWajuLiYkSNH4nA4\nyM3Nbdc1OpqMXIjT474xmTEKShsgyAiGamgIg2IzhIVCTIy/e9qxWpsmsRVA9cHG7Lwyz/NlqWqX\n1bzqpnO5qXPzsfMbDxutF8byeraSyQLWPlC+BcyRYK9QP3+Wk2x75hy9qC5oe9QCVFBhTYayn9RK\nMVBTMKE9ITjOK91PTvYc9YuOjgZULkNYWBh79+7F4XDQr1+/Fs/VNI2goKY6ppmZmTzxxBPU1taS\nlZVFUlISF154IYMHDyYrK4srrriCDRs2cPPNN5+0TwcPHgRo8ZpxcXGu/jnpus7SpUt54YUX2L9/\nPw0NDa6+xcW17z06dOgQjz32GP/3f/9HaWnTFJemaZSXl5/kmf4jwYU4fdZkiCqAQb+AdRtVacHo\nWjgaDQVlMGlS158SaU1r0yTWVPWXneRgdBtt5ViAKuNtQ41caHRgYSxLT6g6APbGkbOo81sftXBy\njl5U7Gh71MJ17V4qJ8Ne0ZTIbU0+yyzUJkZj62M5ztUVDocDg8HAJ598gsHQcjA+LCzM9fUll1yC\n3W5n48aNbNiwwZXbkJmZSVZWFrt27eL48eOudm9w5oPMnj2bJ598kpiYGAwGA/fddx8ORyurcppx\nOByMGzeOsrIy5s+fT3p6OlarlYKCAmbMmNGua/iDBBei/Vw7nxpUGeyR5wI67N0ABZrKt5g0Vu0S\n2t059yWx9FS/oN1zMGx2qLKDoxvkpXRT5eXQK7JpH5AImvYHqURNiYCPpkFa4xy9KM1Rwe/JRi2c\nrL3V6pG2Ri1c13YbvTCYvTpq0R5paWnouk6fPn1aHb1wN3z4cMxmM+vXrycrK4s//vGPAFx66aW8\n8sorfPHFF2iaxqWXXnrS66SkpACwZ88e+vTp42ovKiryGFkANW0zduxYj7wRgLKyMuLjm/7oaKv4\n1tatW9mzZw8rVqzg1ltvdbWvXbv2pH30NwkuRPs0L/Vtr4SaAzDEAueNhZBLoeeF8mHp5D5NYq+A\nygNQb4DP/wVbC+BYEFjD4OIRcP31EGqVOhidmHsdi9yd8K//wHVj4bw+agTDOQ3ivhoEfDQN0hZL\nT6jOVx/+Jxu1cDJHQMyQ9o1AOEcvGmq8OmrRHlOmTGH+/Pk88cQTrFixosXjJSUlxDRO0wYHBzNs\n2DBWrlzJoUOHPEYuqquree6550hLSyMxMfGkrzlu3DhMJhPLli3jyiuvdLUvWbKkxblGo7FFDYtV\nq1ZRUFBA//79XW1Wq/o3KSsra/F8oMUIxdKlS8+4GmhHkOBCtE/zUt/B8SpDvCQbEkZCyhX+7mHg\ncQ4lW5PV3PXnq2D7evXLPT0Iqgph0xvAbhg/WXIwOin3HAtdh1W7VI6F4wA0pMAFmgowHKgRC7/t\nD2KyQPRgMLYjsHBq74eXyaoSRO2VHTpqAdC3b1+efPJJHnnkEfbv38/kyZMJDw9n3759vP/++8yZ\nM4d58+a5zs/MzGTx4sVERUVxwQUXABAfH096ejq7du3ijjvuOOVrxsXF8cADD7B48WImTpzIhAkT\nyM3N5ZNPPvEYjQCYOHEif/7zn5k1axajRo1i69atvPXWW6Slee4QnZaWRlRUFC+++CJhYWFYrVYu\nvvhiBgwYQFpaGvfffz/5+flERESwevXqFkFIoJHVIqL93Et9G0yq3LflHIgd5u+eBbagaKi1wu4t\nYOoJETFgiILwc8CaBLu2qSqnElh0Su45FkX74eA2iAmF/EOw52hTRc5av/ayUVA0GH20UXt4P7UU\n2w9/TT/00EOsXr0ao9HIwoULefDBB1mzZg3XXHMN1113nce5mZmZaJrG6NGjW20/1ZSI06JFi1zl\nuv/4xz+yf/9+PvvsM6xWq8eIwiOPPML999/PZ599xh/+8Ad++OEHPvroI3r37u1xnslk4o033sBo\nNPK73/2O6dOns27dOkwmE2vWrOGiiy5i8eLFLFy4kPT0dFeBrUCldfaSo5qmDQGys7OzGTJkiL+7\n0zW5ci2Asm1QdVAFFdWHISwN4ob7t3+dwY7NsGw+xKZB+AlwBKldVe1VUFwAv/0bDBzq716KM2BD\nVd4M0+G9f0HuNgi7GA6UQK/+MGc0hDR+hljw7h4hOTk5ZGRkIL//RFtO9TPifBzI0HW9fWtj20Gm\nRcTJtZZrcWI3VP6s/gJKaF+U3+0lpIKjNxRpEBoO5jKoN4O9UNXBiI6VvUg6kdb2Csk/AD/thqQ4\nCD0G5joo2gTxcXDRAHVuh+ZYCOFHElyIkztZrkX8yPZlnQuV6DryMvjgAzBFQY+GxgS4IzDoUmj4\nCY67nS91MAJW8zoWtcBWHb47AMfiIdEAjlqwmuBIJWz4HEal+2W2QAi/keBCnJozIdG5nFJyLc6M\nc4nuN99AXiXE1cF5Y+CSTKmD0Ym0VsfCXg6lpUAkHDoIRjs4TBAcBAcOwNGjkJTkx04L0cEkuBCn\n5iwKVXlAfeA57Go6JCzV3z3rXEJDm7ZsP7YfzMegx8CWdTBkL5JOwblXiAFV0+KyTKjUoX8dBDem\nsoU6YKgDevTwY0eF8AMJLsTJOZM5K3UoOAjh5aq8d6j8tjxjsbHqaKjxrINhsqj9HML6qIBOdApB\nqOWmafEdVM5biE5AggvRtnobHNkIX30MO7aDVgQRdug5CC6PVOvZZej+zDWvg1FbDHq9ynGpa7Zf\ngCR4+o178iY0JXA23+XU73UshAggElyItpks8NUm+H6jKvwUEQU1RyFnB7AJZlzl7x52Dc5pp9Jc\nNUpUvrXlOZLg6RfNkzedbduAMGAwKrBwtgshFAkuRNuKi2HTXoiMgchIVZfBHAR1je0TZW8Mr3Hu\nRYIDaoo893OQBE+/aZ68SeNtGGoKpJym0QvowL1ChAhwElyIth3Pg8oqSIwGUznUR4CpSq0WKbND\nSYkEF97i3IukoRqKNkqCZ4BxnwIJQY1YVOCZXwGSYyGEkwQXonX1NjDmQ88TUF8OZjuYS9RjddUQ\nkQSNmwEJLzGGqMN9ZU5VAVh7AQYpstVBmhfIqkUtNzXQNAXiHMmQ/AohWifBhWidyQJxyTAwHdb/\nCBghqg6qGuCwAS6/TEYtfMWZ4GkrgOqDoAH2ZpsUSQ6GTzTPsahB5VeEorZNP5+mAEMI0TbZuEy0\nzZoMl14Ol46GGgscq1G3l9/YVBBKeJ8zwbO+CqypYAhWRbacR0OdWlEigYXXuedYhDceoY2PVRBg\nm5CJgNSnTx9mzZrl7274nYxciLYFRUNUXxhrgMwr4PhPkDAYUi/zd8+6PmeCp6WnFNnyA/cCWRGo\nwKIalcRpbzxHkjdFa7QzrPN+5MgRXn75Za6//noGDRrk5V51PAkuREvuu6AGRYFeB+YKSOoJPTr/\nD32n4EzwbKvI1gkHlOxReS8yPeVV5eUQHqm+DkJNhdiAE0iBLOE7hw8f5oknniA1NVWCi/bQNO1u\n4AGgB/AjcI+u69+3cW4P4O/AUKAf8P90XZ/n6z4KN813QQWoPgJVhyBigBqiFx2jtSJb9Q74cC18\nuxWqKsEaBhePgOuvh1CrJHmeAfcEztyd8K//wHVj4bw+KriQAlmiI+i67u8ueJVPcy40TbsZFSz8\nF3ARKrj4VNO0uDaeEgwcA/4M/ODLvok2OHdBbbA3zfFHDARzNEScK/P8/uDMwagthvW5sOF9iC6E\ndNTtpjfgf/+igsJ62ykvJ5o4EzjXA+t0eHWXSuB8Lw+ydTUd0t1yLGpRIzWtHR35PixYsACDwcDP\nP//MzJkziY6OJioqilmzZlFTU9Pi/DfffJOhQ4disViIjY1l2rRp5Ofnux5ftmwZJpOJiooKV9vf\n//53DAYDDzzwgKvN4XAQHh7O/PnzT9nHJ598kt69e2O1WrniiivYvn17i3NKS0t54IEHGDRoEOHh\n4URGRjJhwgS2bNniOmfdunUMHz4cTdOYOXMmBoMBo9HIG2+8AcCGDRuYOnUqKSkphISEkJyczLx5\n81p9HwKFr0cu5gIv6br+BoCmab8FrgVmAc80P1nX9YONz0HTtF/7uG+iLc13QTWGQNR5EHW+v3vW\nfVmTobgANh2EiB4QbYD6cAiPAnso7NoGl06GBAn+Tod7AmfBfsjbCgkpUFAAu45B78SmqY/OnGPR\nvIS5U/OpndYqkrqzACPomOkgZ+7C1KlT6du3L4sXLyYnJ4d//OMfJCYm8vTTT7vOXbRoEY8//ji3\n3HILd955J8ePH+e5557jsssuIzc3l4iICDIzM9F1nQ0bNjBhwgRAfWgbjUaysrJc18rNzcVms3HZ\nZSfPLXvsscdYtGgREydOZPz48eTk5HDVVVdht9s9ztu3bx8ffvghN910E6mpqRQWFvLSSy8xZswY\ntm/fTo8ePRg4cCALFy7k8ccfZ86cOWRmZgIwatQoAFatWkV1dTV33XUXsbGxfPfddyxbtoyCggLe\neeeds3+zfcBnwYWmaWYgA3jK2abruq5p2lpgpK9eV3hB811Qa0vUDqiymZb/BEVDQ7IqXhZ9DujH\nQWtQVVPDQ6G4BGqs/u5lpxWkQ+5G0CvgvBrYXQBVFhh1HVgb8/M6a47FyQKG5sFCaxVJ3a9jo2WQ\n0t7A5UxlZGTw8ssvu+4XFRXx6quvuoKLvLw8FixYwFNPPcVDDz3kOm/KlClceOGFLF++nIcffpjB\ngwcTHh5OVlaWR3Bxww038N5772Gz2bBYLKxfvx6DweD6YG9NUVERf/3rX/nlL3/JBx984Gr/05/+\nxFNPPeVx7qBBg9i9e7dH2+233056ejqvvvoqjz76KAkJCYwfP57HH3+ckSNHMn36dI/zn3nmGYKD\nm97N2bNnk5aWxqOPPkp+fj69evVq79vZYXw5LRKH+vkqbNZeiMq/EIHIfkIVazJHqZGLyjx1K4GF\n/8UlQVgYlNSqUQtjtWqvLQZDLCSk+rd/ndj+/bBjByQmgtEBSdGwfyfk7WzKs+iMgQW0vrw2vPF+\na8ECNK2WcT9a+/7dp5WaH5s4+2kUTdOYM2eOR1tmZibFxcVUVlYCsHr1anRd56abbqK4uNh1JCQk\n0L9/f7766ivXtUaNGsX69esB2L59OyUlJTz88MM4HA42btwIqIDj/PPPJyIios1+rV27Frvdzj33\n3OPR/oc//KHFuWaz2fW1w+GgpKQEi8VCeno6OTk57Xof3AMLm81GcXExI0eOxOFwkJub265rdDSp\ncyGaOJM5j2epzbOqj0LRf9Rt1X6Zz/e32FgYPRoKC+FIHdQ1QMVhKC+BC0dBuEkFhs7DPSlXuDTP\nKajW4ZtssNVBcDDY7eq2pgbWroWukmfXPGDwRrB0JoHL6UpO9lx2HR2t/tApLS0FYO/evTgcDvr1\n60d8fLzrSEhIYOfOnRw7dsz13MzMTLKzs6mtrSUrK4ukpCQuvPBCBg8e7Joa2bBhg2taoi0HDx4E\noF+/fh7tcXFxrv456brOkiVLOPfccwkODiYuLo6EhAS2bt1KeXmz3Y/bcOjQIWbOnElsbCxhYWHE\nx8czZswYNE1r9zU6mi9zLopQP1uJzdoTgaPefrG5c+cSGRnp0TZt2jSmTZvm7ZfqupzJnDUlqr6C\nIRiMwSrnQoo2BQZn8bJvvoG8SkiohmHnQ2YfFRS6kyqeLTSfIqgFNlbAj0FQlw4HC8DQAA4TBAfB\ngQNw9CgkJfmty52C+94rTnVeurbR2Hqmi3N1hcPhwGAw8Mknn2AwtPx7OSwszPX1JZdcgt1uZ+PG\njR5BRGZmJllZWezatYvjx4+fMrg4Hc58kNmzZ/Pkk08SExODwWDgvvvuw+FwnPL5DoeDcePGUVZW\nxvz580lPT8dqtVJQUMCMGTPadQ2nlStXsnLlSo82XwUnPgsudF23a5qWDVwBfAigqQydK4DnvP16\nS5YsYciQId6+bPfjnswZHANoqs6FFG0KDKGhMGMGTJwIx/aD+RhEhKudVIPjm86TnVRb1TynIBhI\njmgsQuuA/nUQ3DhSEeqAoQ7o0Q0ncVubzgjUFTNpaWnouk6fPn1ajCQ0N3z4cMxmM+vXrycrK4s/\n/vGPAFx66aW88sorfPHFF2iaxqWXXnrS66SkpACwZ88e+vTp42ovKipyjag4rV69mrFjx3rkjQCU\nlZURH9/0f7at4ltbt25lz549rFixgltvvdXVvnbt2pP2sTWt/cGdk5NDRkbGaV/rVHw9LfIscKem\nab/SNG0A8CJq+vJ1AE3TntY07b/dn6Bp2mBN0y5E7Woc33h/oI/7KZxcyx4bNymrr1L3JecisMTG\nwsChkDpWreIxBauA0GBqXOUjVTxPxvmXdgSQocFVcTA2AW7pBbf2VsdNKTAgFc6w4GLAqUUtq3Ue\nrQULRtQv6DpU0TD3o47AXDEzZcoUDAYDTzzxRKuPl5SUuL4ODg5m2LBhrFy5kkOHDnmMXFRXV/Pc\nc8+RlpZGYmLzAXdP48aNw2QysWzZMo/2JUuWtDjXaDS2qGGxatUqCgoKPNqsVpWQXVbmuY+Qc+Sm\n+QjF0qVLz7gaaEfw6VJUXdffbaxpsRA1HfIDcLWu68cbT+kB9G72tFzA+S8xBJgOHAT6+rKvgqbK\nnM6qnFV5oNdLYBHIWttJ1VnFU/7d2qWrF8lyBgw2Wk5VNA8WglGrR9rKlWhrBUjzQKUjRzn69u3L\nk08+ySOPPML+/fuZPHky4eHh7Nu3j/fff585c+Ywb15TLcbMzEwWL15MVFQUF1xwAQDx8fGkp6ez\na9cu7rjjjlO+ZlxcHA888ACLFy9m4sSJTJgwgdzcXD755BOP0QiAiRMn8uc//5lZs2YxatQotm7d\nyltvvUVaWprHeWlpaURFRfHiiy8SFhaG1Wrl4osvZsCAAaSlpXH//feTn59PREQEq1evbhGEBBqf\nV+jUdX05sLyNx1r8K+q6Lkmm/uBembOiAo7vAGMpxJ2rkjmD42SIPZC5V/HU7SpArGs2l9pNt2lv\nzxbqXdnJAobWgoXTSfQ8ncDFlx566CHS09NZsmQJCxcuBKB3795cc801XHfddR7nZmZm8pe//IXR\no0e3aN+9e/cpp0ScFi1aRGhoKC+++CJff/01F198MZ999hnXXnutx4jCI488gs1m41//+hfvvvsu\nGRkZfPTRRzz88MMe55lMJt544w3mz5/P7373O+rr6/nnP//Jr371K9asWcO9997L4sWLCQkJYcqU\nKdx9990MHjz4TN8yn9M6e8lRTdOGANnZ2dmSc3G2jnwHn70JWw6q/Swi7dDvPLhqNiQN93fvxKmU\n/ggluaA3QGgrw7rdMMGzrS3UTah511+gAoxa1IfjpXSukQvnfLk/f//5us6FODun+hlxy7nI0HW9\nfWtj20E2LhNNPtsM326GiASISAFbMXy7DdgMMyS4CHjOnVRxqARPS8+mx7ppgmdrCZzRqByCMlR5\n765QgdOfJIAQrZHgQijFxfDNDxB+DsQZoT4ILFaoD1HtE4tl981A59xJtaEaijbKNu1u3Gs8DEF2\nORXC1yS/QSglJVBdCqFxQAOYytVtaJxqd8u4FgHMGNJyxU9tiaz4cRNEU6BhofNX4BQiEMnIhVAi\nQ6BHDTgOgFEHcznYI8FRCT1M6nHReXgkeNarImjdJMGzuydwChEIJLgQSkJvOH84fP9vcMRBdCSU\nmqDyOAybqB4XnYdz9KI0Vy0vLt/a8pwumOB5OgmcQgjfkeBCNJn8a6AUtu6Bgw1gMcOw0Y3totPp\nhgmeksApRGCQ4EI0iewJ182AYVugLgyCKiFpkGoXnU83TvCUBE4h/EuCC+HJmgxRBaCZQA/u0h9A\n3UJrFTyrCsDaC0rKoHQ/REdDTEynzcFwz7HIL4baWM8ci65egVOIQCTBhVCcpb8xgCkSKnZCxAAV\nZIjOz5ngaSuA8r2wfh3s2Kf2FQ8JgYHnweXjoeclnWqqxD3H4uBB+OgLSL4W+iSqfUPOp3skce7Y\nscPfXRAByl8/G/LJITxLf4Oap68rBtshoL7LJf11S84Ez/Lt8OMR+D4XQntCdCJUVsL3/wFiYMZV\n/u7paXHmWJh12LYRDm0HRyqkJECFph5z0HUTOOPi4rBYLNx2223+7ooIYBaLhbi4uA59TQkuhAoc\nzFFQU6KS/oLj1QdPbZFql8Cia7AmQ3EBbC6G8BiIjATdDLFGKK+BTXs7bbG0w/th7zboGQ3H9kLh\nAIhMgkrUdAh0zQTO5ORkduzYQVFRkb+74nMVQDZqyst9NKq+8fYiILSjO9VJxMXFkZzcsVPcElwI\nxTls7kz6k227u56gaGhIhmIDxCSCsRrqzeo2KBHKalWxtE4WXOg6fPcd1NVBWm+o2gcnNsCoG2G0\n1vUTOJOTkzv8g8MfbKilxeGoRF2nGlSy7kVIPk0gkQqdQpGqjt1DXBKEhUGJBroRDDZ1W6Kp9pgY\nf/fwtOUdhF27ILFxr7akONi3HY7lSQVOIfxFgguhci3qytUUiKMOKvPUrQQWXU9sLIweDQVlUFgH\njgp1W1Cm2jvhqEV2DtjsYLRCta5ubXbIzlaPi66jDjVS0fxovt278D+ZFunumidzVh8FWx5YkqFq\nPwTHSc5FVzN1qrrd9CUcKgOiYdLYpvZO5PhRKM4DkxUOlTa1m6yq/fhRsCb5r3/Ce2qBXagkXrNb\nux015ZWJTIsEEgkuurvmyZyGYDAGq9oIkszZNYWGwowZMHEiFB1RUyWdbMTCKaUHLJoENfaWj4WY\n1eNCiI4nwYXwTOYMjgE00OskmbOri43ttEGFk6bBgFR/90J0hGAgHbDSMqGzCsmpCTSScyFaJnPW\nV0kypxAi4ATRVNbd/egOhdI6GwkuhGJNBqNZbdFtNMuohRBCiDMmwYVoTOY0gCkCqg6pWwxNSZ5C\nCBEgKlE73DqPClSyZ1etwtpZSc5Fd+e+WsReqUYubPlgL1ObWEnpbyFEADCiVonk0DKQCEblYmQi\nuReBQoKL7s59tUh9NNQ0QHA0GKrAIqtFhBCBIRgYgqrGGdR4v6wMoqLUctR6mnbHFf4nwYUAQzx8\n9d+wdQ9U2cFqhgv6w+SL/d0zIYRwCUYlcIYDh/fBhx/AdZOgZ18VdIjAITkXAt7/HL76AYLt0KOH\nuv3qB9UuhBABRtdh40bYvUfdSiXWwCPBRXdXeAC+/QqiekJUOITa1G3kOfDNN1Bc7O8eCiGESx2w\n8wBs2wtxvdTtroNSAjzQSHDRndXboOAbCN4P8TVgrITQfHUb2wC2MrVLphBCBIBaYKcO7x+CI8lg\nH6Ju/zdPtcuKkcAhwUV3ZrJAdC8IDYIyB9jjoC4GHCFQblcJnZ1wl0whRNdVeBTy8yE6CtDVbX4+\nHDvq754JdxJcdHfnDIIBF0DZcSiqhqowKK6F/OpOuUumEKLrCtKhbBNYdkBKISQeVLeWHVC6ST0u\nAoOsFunugqLhqluABvgxD0oKQUuACdd1yl0yhRBd19GjcPwwWAxwLK+p3WJW7UePQprsghsQJLgQ\nENsfrrwaRtjgRBn0vhx6pPm7V0II4aFHD5hyPQTVQbDbKEWtBnVB6nERGCS46O7cS3+bjkDKAIiK\nU+3mcH/3TgghXDQNYpJUpU73zcrqUIW0NP90S7RCgovuTEp/CyE6kXrgIFDeymORjY+LwCDBRXfm\nXvo7LBVCe4IxGGwFUvpbCBFwTEBK4637HiK1qMBCPtACh/xbdHfWZKguAEcdmK1qNMMUIluuCyEC\nUhCq/HeIW1sNUv470MhS1O4uKBpCz4HaxmJZtSXqflC0f/slhBCi05LgQqhRCqNZ5VwYzTJqIYQQ\n4qxIcNHduVaLRELVIXWLobFdCCECTyVQ5nZUoPIupPx34JCci+6s+WqRumKwHQJ7qawWEUIEHCNq\nGWoOLQOJYMAKZOKZ7Cn8Q4KL7kxWiwghOpFgYAgqeTMIzyDCjlox0uCHfomWJLjo7mS1iBCiEwlG\nrRSRFSOBzec5F5qm3a1p2n5N06o1TftW07Rhpzh/jKZp2Zqm1WiatlvTtBm+7mO3JqtFhBBCeJlP\ngwtN024G/g78F3AR8CPwqaZpcW2c3wdYA3wBDAb+H/APTdOu9GU/uzX7CTU14qiDyrzGEYwoSegU\nQgSsOtRIRfOjzp+dEh58PS0yF3hJ1/U3ADRN+y1wLTALeKaV838H7NN1/Y+N93dpmnZJ43U+93Ff\nux/3hM7qo2DLA0sylG+VhE4hRECqBXahcivMbu12VMJnJiC/tfzPZyMXmqaZgQzUKAQAuq7rwFpg\nZBtPu7jxcXefnuR8cTacCZ0NdogcAOH91W1D4+iFBBZCCCHOgC9HLuJQgWRhs/ZCIL2N5/Ro4/wI\nTdOCdV2XZcze5kzorKyFE5FALVgloVMIEZiCUR8gVqCmDKKiVHsNUIUsQw0UXWa1yNy5c4mMjPRo\nmzZtGtOmTfNTjzqJhhD4PBt2ZkGZAaIcMCATpl7u754JIUSrgoAj++HT9+G6SdC3r2q3+7VXgW/l\nypWsXLnSo628vLU9Zs+eL4OLItS0WGKz9kTgaBvPOdrG+RWnGrVYsmQJQ4YMOZN+dm/vvgsfbYK+\nJjgnHKpOqPu8CzNkoY4QIvDoOmzaBLv3wMaNkJoKaP7uVeBr7Q/unJwcMjIyvP5aPsu50HXdDmQD\nVzjbNE3TGu//p42nbXQ/v9FVje3C24qL4duvID4BIhIhtFrdxieo9uJif/dQCCE81AJ78mDbQYhJ\nhameyxkAACAASURBVB8PwI8HVUlwETh8XefiWeBOTdN+pWnaAOBFVCLv6wCapj2tadp/u53/ItBX\n07S/aJqWrmnaXcCNjdcR3na8AIz5kFQB5gowVqvbpArVfrzA3z0UQgiXWmCzDp8fgMJeUHMRHOkD\n/5MPP+pq9YjRv10UjXyac6Hr+ruNNS0WoqY3fgCu1nX9eOMpPYDebucf0DTtWmAJcC+QD/xa1/Xm\nK0iEN8SfA+ZIsFWCoRfUR4BuVPuLmCPV40IIESD+f3t3Htz2fd55/P0FCYDgfUqk7sOHpNiyLfmM\nnMN2Y9eJG8dt6lZpGm8nu91umkw2O91k/+ix2W4m7Uy2nR7b2WzSpmmbqE3S7SRZx7HrxNn4lG0p\ntiXrsi5SB0lJvC+c/O4fD2CAFCmJFEAA5Oc1gwH4ww/ADz9RxIPv9/k+Two43gmjL8KmOqhNQNMY\n9J+GyBrYtkYJnaWi4Amd3vu/Av5qlvt+Y4ZtP8WWsEqhtbTAzffBS/8AyQvWT2T8AgyPwJ0P2/0i\nIiXCe9izF1KD0FALjEIDcGEA9r0KodUo96JELJrVIjJPj/4G0GerRXqitlrkzgfT20VESkdPj11C\nYTh7Nrs9FM7et7GjeMcnWQoulrpIBHZ+Eo5fB6PjUFsNG+6HUKTYRyYiMkV7O/ziIxCKQ9hnt8cc\nxEN2v5QGBRdLXWIECEDzKqg8BPWr7OfEiJUAFxEpEc5Bc4clboZytsexGheaESkdCi6WstzeIolR\niPdZMmdiQL1FRKTkJIFOYKayTw3p+6U0KLhYyjK9RaL9ULseIiugIgzjZyy5U4GFiJSQSmBt+jp3\nVUgMCyz0gVY69G+x1GV6i0zGIVhjoxmV6i0iIqUpBNQBVTnbosBIcQ5HZlHoIlpS6kJNEFkJsX77\nOdZvP4eaintcIiJSthRciAUSPg5jXXYdaoT4UDrZU0SkdMSxkYrpl3gxD0ouommRpS45DmMnYKIb\nxk5BzWoY3Gf3KalTREpIDDiMVeoM5mxPYGW/34X1l5DiU3Cx1GWSOoNNUBuGug0QrFdSp4iIzJuC\nC8kmdboOCDcpqVNESlIYuB6o4eKEzjHUV6SUKOdCskmdyTH7WUmdIlKiQlhgMf0SutSDZMEpuBBT\nswYqghDrs2uNWoiIyDwpuJBsCfDKBkvqrGzg7RLgIiIlIoZNgQwBgzkX/aUqPcq5WOpUAlxEykAM\n2Au8lb6dKwzcgq0YkdKg4GKpUwlwESkDKWzJ6VamfnDF05ftKKGzlGhaRCy/ojJsJcDHEtB1DMYT\nyrsQkZJTCzQCDNp1PRZUKLAoLRq5EFsV4lrhiW/A610weQHcMrg5Co8+CpFIsY9QRORtx4/D974L\nH3wYVmwo9tHITDRyIeapZ+GVFyEyDm0tMFkFj38HvvX1Yh+ZiAhg0x8THn76Mhw6adcTXqW/S5GC\nC4Fzp2D/T6AtCO3DEInCykm4Jgn7H7f7RUSKKFP6+/EeeD4B7i67frzXtk9P8pTiUnAhMBSF4aRN\nj8RbIdEGqRqoqbLtQ9FiH6GICN7DW29BIgmNjXb91hHbLqVFwYVAczNULIPhSUg0wmQEXApGY7a9\nubnYRygiS1wYqO6EiWdh8zCsOmPXE89CdZcSOkuNgguBlha4417ojsLIeYjHYaTbfr7jXrtfRKSI\nvIc30iV5airAT9h1YgTe2KPRi1Kj1SJiHn0UGIOD34O+TqgOwz0fTm+XJSsxAn4S+vthYACammwk\nywWsyFqBxLC6BgB9fdn4tgJ9Q12qenrsEgrD2bPZ7aFw9r6NHcU7PplKwYWYSAQ+8utwci2cfw3a\nboa1dwNxm9gs4AeJlKjkOHS/CM88AQcPQDQKVVWweQvc8yCsuLsgRdZiwG5gHOjshKeegvvvh7Vr\noRq4AwUYS1FTO3zgESAJoZxRiiQQDEJ7e7GOTGai4EJMpgx4cAQagnZ9/lm7T2XAl6bKanhmd3qJ\n8gpoWg6jo/DKC0AzPHZ/QV42hQUWQQ/7X4TO/bC/Dq5ZA+MuO6IhS0cM+JmD4Y7ZS3/rw6y06N9D\nTKYMeKAfWu+0EuCgMuBLWV8f7D4KDc3Q0AA+CC0Vtnpo91F4qK+g+ThnT8DR/bCyxa6774DW9QV7\nOSlhKv1dfpTQKVmZMuDOQaDSyoFXVqkM+FLV3w+DCQgth4oJ21YxYT8PJuz+AvEeXn7ZcouXL7fr\n3buVtLfUZUp/Zy4q/V26FFxIVqgJIishlv7QiPXbz6Gm4h6XLIzECMSHspe6SmgIWSDhKyAwbtf9\nDmprC7pEuasTDh+2wALs+uBROHrKpkxyLyqeJFJ6NC0iU4WaYPIIjHaBT9pUSXyo4KsDpMgyOTeJ\nkanb72yC516F823QnIQLYTgzAQ8/XLApEe9hz17rnVdRY+WdqYfeevhBF6xaDRGX3V9JnotfLH0J\nTtuust+lS8GFZCXHYewETPTAeBdUr4GhfXafkjoXt0zOTbQfqldkt++4HWi2HIuxs0ATPHxvQZco\nn++Bvi6orIFTA7YtVQmshtEeSF2AujbbHsNGL5TkuXjFgFeAfdgHVm6AUQGob1lpUnAhWZkPmFCj\nJXTWrodgvZI6l4qaNTBxJp1rU23BZnUD7PwkPDQJF7qhtaPgRdXWtsMXHoZoIrttwsGeCDQHYF0r\n5Axc6NvrIpcColi+RW4QmQAmgCosyJDSouBCpsp8wLgQhJvsA0ZJnYtPpjjWFIH06MV5Cy5i/VC7\nzqbKWliwSq3OwaZpq0LGgSGgjosDi8zoRS4V21pcQsBN6euMKDAC3Ib+rUuRgguZKpPUOXrSgovc\nDxhZHGbLr3hbCmJ9UBEs6aAyDrwJDAIe+waboTyMxSfE1H9jsNEL/RuXJgUXcjEldS5us+VXjJ+B\nuo12e+gANGwpuaAyd2VIFBjF/ojVkf3gUR7G4qJkzvKk4EKmUlLn0jBTfkXu9FditKRGLSqw0Yhx\nsh8qMaz0c1P6vtwhc33wLA5K5ixfCi5kKiV1Lg2501/T8ysAWrZDxfRB6OIJY9McuaMR49h0SANT\nAwtZPJTMWb4UXMjFlNS5uMyYvIkFEhVnZs6vKKHAImOmufUqLh6xiKYvuUmeSvAsX0rmLE8KLuRi\nmW+13W9AfARCo9CxteTm3+UKXCp5M1gHoRYYPV6S+RVXKpOHEQcOYB86SWxVSeaDRwme5S0ERAeh\nsTG7TcmcpU3BhVxsYgK+9yM4/DhMxCESguvfD48sh0iNkjrLyaWSN6sbbbRiMlmWo1LT8zCiwAD2\nRy3TdyKEEjzLWSaZ88xJePr78IGHYP165dSUAwUXcrFv/T089y+wahLaEjA8Cbu/A5yGBz+kpM5y\nc6nkzVBTyeVXXKnpeRjj2GhFLUrwXAwyyZxveHipC45UwmgnvGcdVDolc5a6gjUuc841Oee+4Zwb\ncs4NOOe+6pyrucxjHnHOPemcu+Ccm3TObS3U8cks+vrg+Vehvh1qlsHkMqjaADUdcHg/jKHAotxc\nriFdGQYWGWEskMhcwlychyHlKZPMOdoNZzttSuT0KTjTa0uQlcxZ2grZFfWbwGbgPuADwLuBL1/m\nMTXAs8BnsURwWWj9/TA6ClUrYbIaks0wGYG6CIwlIHrJ+FBKQaa7ac8JOLjXrkON4BNlURwrnzLT\nJZmpkVN96qRaToIeRp6DhkNw47hdTzwL7/BK5ix1BZkWcc5tAh4Atnvvf5be9ingcefc73jve2Z6\nnPf+H9L7rmVqlV9ZKM3N1k67PwY1dRAchMkq+1AKtMCy9Zd/Dime5Dh0vwjPPAEHD0A0ClVVsHkL\n3HY9hEeh+ZayTd68ErkJnm9i33KTQFcX/ORJuP9+2LxWCZ7loKsTjh6EFc1QmbTr4wfgXBeE1xb7\n6ORSCjVycRcwkAks0p7GRiPuKNBrSj60tMCOHdDbC72jEI/aROdQP9z8TqirvETZaCm6ymp4Zje8\n8iKkaqBprV2/8gK80gV11y7aUYtMgmccWzEyjJUGB2jycPAl6NwPr78MY14JnqUu6mH36zCWhIoa\nmPB2PR6HPXvAa2y7pBUqobMdOJe7wXufcs71p++TUvboo0AM9n8fRs9CfQKu2wrvWgfnn1WlzlLW\n12ft0RuaoaEBfBBaKmAoCrvPwIPrFu2oxUwJnh4rDd5zHE68AStb4OgBG8VA33xLVgx4sg8OBGBi\nE+zPLdNyLZw5Bz09sLGjWEcolzOn4MI590Xgc5fYxWN5FgvuM5/5DA0NDVO27dy5k507dxbjcMpb\nJAKP/SacuB66X4FIANpvVKXOctDfD4MJaFsOFROQDNp1aDkMxmBoHJYV+yALZ/o0RxUQ9rDnJYjH\nYfVqONJl33w/ugZNvpaoFFDdAu+7C+LJ7Paks8v2FKzU19Q527VrF7t27ZqybWhoqCCvNdeRiy8B\nX7vMPseBHqb9CXPOVQDN6fvy7k//9E/Ztm1bIZ566Vq5FcJjqtRZ6nIrcNZVQkMIhhJQOwmBcfAV\n0O8sl6a5ubjHWgQnTsDBg7B8uf3c0gGHTsBrh+GWTdn9VMWztIQd3Nt6cWXOUWx1QPmucSqemb5w\n7927l+3bt+f9teYUXHjv+4C+y+3nnHsRaHTO3ZKTd3Ef9j1h95W+3FyOTQog1GQFmEZPQiBooxY1\na4CAfaCpmFbxzVSB884m2P0SjIShuhrO1cCZCXj4YcupWUK8hxf32Lx9aw2MOhhaC+cH4a8Pwy9f\nDy49eqEqnqUhs7InytRGZQEsoFBlzvJQkJwL7/0h59yTwFecc/8BCz7/AtiVu1LEOXcI+Jz3/rvp\nn5uANcBKLBDZ5JxzQI/3vrcQxyqXkByHeD+MHIHRo/bt2AUgMai8i1IxUwXO+z4EJGHfSbgQBarh\n4XvTuTRLRwUQ7YPT5yHQAKcGIFUJg/VQlYKBTohfgNY2VfEsFTHs2+cAsB+IkB25qAKuKdJxydwV\nskLnR4C/xFaJTALfAT49bZ9rsaaGGR/Epl18+pKZHPo88N8KeKwyk8pqqF4Nw29BcgRqN1qXVOVd\nlJbpFThDAXjfg/DA9TA0Aa0dS27EAuzb7YMtVrk+ni7ROeFgbxXUeWisgBWt2bQLVfEsvhQW5IWw\nwCKIBYkJbPXPBIUtziT5U7Dgwns/CHz0MvtUTPv568DXC3VMMg81a+wbcfQC1KxKf4Ap76KoLupy\nGoDKBhjvgvrrsu3TmzYu+bVZVQ62rMv+PA4MYStIMnP26qRaeqqw3jBRLOBIYoFFHEvcU2XO0qfe\nInJpoSao3wQcsdUiY6ftg2uRLmcsebN1OU2MWnBRUbukKnBerTg2/J75VqxOqqUhBNyADXlDNpFz\nBxYY6t+k9GmESS6vZo1lvY11gY9bKen4kF1UUGthZXIsUgkIt2UvgRDUrIfU6NS+ITKjGNmRiuH0\ntgjW9KwO+3BTDsbCy3RBjZINLMA+qDJ9ZBRYlAeNXMjlBcIWSAwfgprVMLgve58SOxfebF1O6zfD\n+FmNWlzCTG3aJ7DAop6p3VSVg7GwMl1Q92EfTLkrRSpQF9Ryo+BCLq+y2ubyJ3rtAyxYb9uV2Fl4\nF+VXAATSK0TO27nP5FjUrodIR1l3OS20K2nTPr3ZWYZyMAor0wW1lqkjRgksAFQX1PKi4EKuTOMN\n6Y6aVTA8CoO9UF0B7fqWXDCz5Ve8LXVxl1MFFpc1PUDIbdM+PQfDk038VA5G4YWAm4DxQWuxDhZw\njKAuqOVGwYVcmVAT0ABPfAP2n4HJPqAVtvbDI78E9Yu4pnSxzFTDAmzEqG6j3R46AA1blGNxlTKd\nVKNMzcHIrCpRHYzCyi2cdeYkPP19+MBDsHG9CmeVKwUXcmWS4/Dj78Hhn0BjLVSFYWAcdv8d0AW/\n9nuaHimE2fIrMiMViVHlWFyF6TkYMZSDsdByC2ft8/DyCTgCRE9Yn71r1f+lLCm4kCszNAGvdUFT\nM9SGIdEENc3gT8FrR+ChCWhRcHHVZqxhkV4C3HBtNr8iM1LRsl1TIVfhUp1Up+dgqA5GYeQWzhru\ngTOd0FwPp07BWz2wqkPLGsuRggu5Mv391vxqWZstg0zVgUtBdT2c9nb/EqwCmVeZHIu+MzAyAnV1\nUF9voxMTnRCsvriGhQKLqzZTJ9XZcjAcEB2ybvbKwcivsIfOfTCZgMYVcKYX9h+Dd7ZDi1MyZ7lR\ncCFXprkZws1wYQA6HOCgchj6U7ZipK5SzcyuVsLBEz+FQz+FIQeRCGy9CXZsthoWyTHlVyyQ2XIw\nLpy0fID7fwE61ikHIx8ytS1On4T+l2FDE9Seh3AMBl6GZa1w6yYFceVGo01yZVpaYMcO6B6BaA9U\nHoNYp+UD3NkEqTftW3dy/PLPJTP71rfgB7uBILS3WSfa556B51+Bltugeo3yKwosk4MRx1YojGAj\nFmD9SN54EY4fhL0vWcdVuTqZ2hZvePhuJ/Qug5HV0N0M4x0QG4fn/hVCOtdlRyMXcuUyXTUP/x1M\nnoZYB9z6brjvPkj1qebFfGRyLPr74aVnoG0Z1HsIDkOwBUKj8FonPFQPLaphUWiXqoPRcwKOvAnL\nVsKBY3DdKbgtd4YKfbueq0y+RXQYhs5bz73+c+ADkApDfRhOnoSeHujoKPLBypwouJArF4nAY4/B\nqRvhxLeg7WZYfq2NViTVzGzOcutYnDkD4RPQ1gaV6eBiMgTVdcppWWAz1cEIe9jzIkRTUHsDnO+D\nH3TBqtUQSa9mUA7G/ASAFfVwz3shlY7qEg6iDrZGYUcK2pd4A75ypOBC5m71NogkYeR4umHWmXRg\nEbAy4S6g3IsrkVvHonkdVDTC4CQsC0K8AQJx6A9Yrktzc7GPdkk7chL2H4WmVTAagoZmG8noXwWb\n1qkOxnxkztkksMHBpjbbHkhvGwHeAyjDqDwpuJD5qV4J556B0SM2rO8CkBi0+9Rv5Mpl6lhUVcPW\nbfDc01BZB5VrINYLp2Pw/oc0alEkFUDEw0s/sw+7+nqIBiBYCQzB6y/CTWsBpzoYc5Fb22I/liyb\nqSdSBVyTvtYoUPlScCHzU73SVjCcfwmab7G+FqB+I5czYx2LBmuX/r6fA/rhtdPQOwz1TfD+92Rz\nXWTBhYG1PVDxPKy6AMnT4K8DH4PWGJybgO4LUN2mOhhzkVvbIoI1KavAKnFmlv1qtUF5U3Ah89dy\nm7Vhr4xAKmo5BD5lQ/2aHrnYbL1CEqMWXFTUwvsegAeuh5FJmwrRiEXRrW2Hz34S4nGYcPBKBGom\nLQ+DIHS3ZleVOLIBhXIwZpaZDolhwUUVFpglsQJmE9goUDOqbVHOFFzI/NWuh5bb4fyzUHkaoheg\najkMpVuya3pkqtl6haTiNgqUGoXaLdC0EZTAVjKcg/WZgTmgB/tQDGMfiifT+0WwVSXqRTK7zHRI\nP9npkEx17zDWVj0O7MCqpCowK18KLuTqNN0Ig/sgeg7CLdCwyVqya3rETJ8GCTUCSYgPQlVrtldI\n/WYYP6sVNyVuei+SKBf3IgH7Bq6W7RebPh0Swc5JIn0JYcFGNTpX5U7BhVydUBM0bYUz34fQOlvZ\nML251lI12zTIRDfEj0D7e7O9QmrXQ0R1LErdpepgZAILtWy/vDAWSGTyKiaxYC1OdiRDypuCC7l6\njTfA6HHrOZIYhXOHIF4PgUFoDizd3IvZpkFi/UDAynnn9gpRYFEWZqqDkelFkmlwFkzfp5btWblt\n1QcHIdAIY1gwkZtr0YRyLRYDBRdy9UJN0HY3HNsFLzwOpzuhvwqCfwubt8A9D8KKu5fmFMlMLdOr\nWm2kYvy0eoUsErm9SOLYH9ZMsmImZFzKS1Vzl57+qBf2vQS33w7LO+w8bUzvo1yLxUOrfSQ/6jbC\n691wfB9EG6H+GkjVwCsvwDO7l05gkRixlTKZy9tLTU/b/bF+iKy00R71Cil703uRjGLfwJNYUBHg\n4pbtmUtshudbrDK5FkEPJw9Cdxcc22/FaGNkp4+Ua7F4aORC8qOvD17ts5bs4WZrDhCJwHA9vHoA\nHjgBLa2Le3rkUi3TM0tNM9MgoSZo2a6pkDI3Uw6Gx759z5SDkVmqOjQEHQ1LIwcjdzqkuxO6j0ND\nG5zohg090NChpaeLkYILyY/+fugLQOt6CPfA5AhUjANhGD0LXU9BYNPiW5qauxokOgFPPAVHXoBh\nB6G6qS3TM0tNM9MgCiwWhenBQRUWRExyccv2WqDrJHz/Kbjn52HLmmxgshhXk+ROh+zz8PIJCyTa\nG+FcFwy+ADt+Ee52mg5ZbBRcSH40N0NtLVxIQl0YKsYgVQ39QaiogdoqS25cTIHF9NUgT/8IXn0O\n2r1V1+xz1jKdUfilT2mp6RJwuaWqlR6eOAL7UjCxBBqf5S49He6BnuOwPALBODQ2w/FD0NsF1WsX\n1/sW5VxIvrS0wI4dcGYQesNWH3loHPqGYOtGqK22Gg/xoYuXZparzGqQVAImgvDGcahaDTXNEKqA\npmWwrMZapsfqbRpEyZuLWmaa5N3py93AjcDNwA1A1wk4fhaa69KNzzrtG3uIxbeaJLcSZ8rD4cPW\nVbaiCpIpCFTBeBL27AHvi3ywkncauZD8yfTA2P1j8GegYRTu3gzvCFpth8FFULlztqJYA6dhPAYd\nLZBIzxwHxtUyfQmabalq0MPLL0MyActa4GwvvPYSbF4L3i2uolvTK3FODEGnh4m1cDwJkQGYrITG\naujrgvM9UNNR3GOW/FJwIfkTicBjj8FDD0HPIYg9D5VjUBG2lRGBCEyctW/7kwn7oC6nBM9LFcXy\nvVAThFgfVK6z7aHzcE4t08U+bI+fgAPHoH4LTAagsREOHoJ/PQu1KxdH0a0Y2amQAez9VADLG+DR\nG2A8ZStp1idsv21RaKq0/i2yuCi4kPxraYGWHXBuErr+DwTCMHYSUjFITUAgaO3Zy2UEY8poRSXE\nBq2apnNQWWPLSxsCcGMcXnoehuO2SmRwUi3Tl7hMDsaYh2dfg1EH4WqIJyzXYngCXjsM711hP9dh\nc9UT2Lf+Econ4TMzWpFZGbIfO+YuoNrBtW1WIGsCSHep5yayq2pkcVFwIYXTeAOMHLc+Iz4BOIis\ngHAbnD8CySaY7LVv9aVaxXP6aEViFEaPWmGscBNUr88WxbqrDqiH50/BiXNqmS5v52CcTrdtXzEM\nF4KQSkIsAaEInBuE4SEbyQgAR7l46SqU9khGDAuETg5Ba0O2hXqIbILrWHpfVeJcGhRcSOGEmmDF\n/XDupzD8FuBgYhBe+F9w+li6imddaVfxnF7CO9wGk0nr/FqzBlLj1hukZg0QgJ0fhIcmLcdCLdOF\ndLfPdNv20QS8HoaJdCp9HDhWDdUN2emQKPaHuVy6rGZGLF7vgn98E955M7R32IhFPbAOe583p/cf\nQZU4lwIFF1JYkQ6o3wQjJyxN/OXDcPR1YBU0LIOxUdj7LFANO++w1STFHsXoPWnBQVOTBQjTO5mG\nm6GiGgKhmYtitaCgQqbIbdt+HVOLbj1HtuhWZvItiI1iZKp8Tu+y2tdnSaHF/HDOza/o97B3L/Sc\nh6MhWN8OFe7igMihSpxLhYILKbyaNdB0EwychUNHobYegq2W7Fk/YeOlR16EY49brsJC52Jkciqi\nE/Av/wQHnoDEMFRF4Pqt8K67IZHTyXQyAQ2brV9I5BoVxZI5uVzRrTgWXLj07dxpkjjQ0wVPPw0P\n3QsfXmfPt9D5GNPzK37UCz+bgOBGODwKN5+BmlXZ405hpdHDWGCh6ZDFT8GFFF6oCdrvgfNPQXwM\nWGmjE5MhCPZDRRsMR2EsAeGBhV1NkptT8fSPYPdLsDwA9R6G4vD8K0AdvOsapnQybdqqolhy1WYr\nugU2pQDZLqtJ4JSHZ47DwSTET0PrWksEXah8jOmrQUJYYbATh8GPQ10E+ifgjYPwnpXQ6OB6bPRl\nB9nAQqMWi5+CC1kYFVXQ/g5wrXC+FlYATMJkBST7oTUAk8dgKAE+bkmgwVpo2mYjGPmeKpmyAqQC\n+k/B/sNQ1wpVjRA4CXXN0BCEfT+DO94BzTdlO5nWrrcpH41WyFWYqTeJI9tRdZJsl9VKoLsHeo5B\nW9iKcPWugjXrCr+yJDMl8woW/MSAN7G8kL4eeGscVtRBPAnV9XD8ZLZvSADrG6Ici6VFwYUsnPaN\ncOMvwHefgIoKaI3BYBjiA3DDOyAStjT6+CDEjtkIRnLUHjvuYXI1tKyYXwO03GDi7dGKUZsM95Nw\n4QCEz0BdupJPqg58hZU0H+iFaMRWvxDIjlYosJA8yP3ArcBWUWQqW8bIlg+v8nD4EExGoXUldPbD\nU0dhx1qYcJDAghLS+9/G1U2ZZEYpuvvgWIuNVLyZfo0K4CxQ6+HYIYj5dDmbAQgGIXoCBl+EHY+o\nb8hSpeBCFtajHwVCVsXz1CBUtMCt18KNbTbdENkAE70QbABXAYPH4bXn4eR5GK6EcBiu3ww//5tQ\n22SBQiY3I/c2ARgYgMF+qI9A5XkLJgBbtdIL0W6oXm1VjVq2QPVPYTQJ9QmIL4dAHKIXoKrGRl3U\nyVQK7FJdVjtPwNnObD22hibrLHp9NzSsgNPYSEcCm0IZwqZTqoGt2B/7/j6ob8n+4c/kPqSm3Y4B\nrwHHu+DJn8CaB6B9OXRjK1jWYSMrI6MweB5CNdCX7tCWDEJjBHp7wPfZYKACi6VHwYUsrNwqnhe6\nobUDAqfhzBPgQlC3EcY6oXoDVETg/30b3jxhSaDtIUj1wfEn4Ien4aYtELsAoVZ77nj69iSw/xB0\ndUIybs+zdiO8YzVUt1vhq9r1EO21QCFUCy1rYeUGeOUsJEMQaIfoGUj0wvYP2qgLKLCQgpsp4RMP\nL++BiRS0VEHcQzAEiTgceRPe2QGTDmqwX/8RLNiIYTkbrwLdvfDqXlhzG2xqza5IcWSDC092KuaM\nt2DmSAz6z8AjyyCcbrIWxD48qmrhPfdY5c1rE/ZcCQfbJ2xGcUORV7RI8Si4kOJoacku14wHm+RP\ngwAADl1JREFUbDVJctgSOavaLdCIV8Hp41DVBtUtUDkAle0wUQ+d3bDlJmunGAgC3nI0XCW8+irs\n6YKGRmgeg/4aeOEU4GBbA1SvhFADRNptOSnY6971YeA5eO0c9J6zxgd3PAAf+niRTpIsdZmEz1P9\ncGoAAvXQMw6BSSBlUxHnB2FoyH7dg+nHTWBBQgQLGLyHU2/ChZMw2QG3tkDIZZe2RrCAwmGjJAng\nQD/0HoO2ajjfZ7kVlelZwwA2PRJ1UN1mAUQH2dUg21BQsdQVLLhwzjUBfwk8hP2e/zPwae/92Cz7\nVwJfAB4ENmCjek8D/8V7312o45QSkFlNMnwYhg7YSozkiHV2GglAYx2kaiF43nIhKpshejDdKOxW\nGD4EOEu07NkLJzstgKithUA31LVDNA5Hz8B1K2HZcivZ3XSTvU6sz6ZkVrwTHlwHD7TDyKSNPzfW\naLRCiiYzTbK9GbbcD3sD2QJcSeBECGodLGuw4GC6IBYE9PRA91Foq4Hz52G4G9atsOcACy4yarEc\nijNd1ty4pQV6k3DwoNWvSDr7g74CaAQ2YUGJVoNIrkKOXHwTWA7ch/1+/y3wZeCjs+xfjRVx+zzw\nBpbX9OfAd4HbC3icUgoqqixRMjEKjVtgrAvCpyG5AoZS0JiyAMNXwHACaqpsqqR6pZUYB7s9vhui\nCYg0QyAK8RZwkxZojJyFVI2NUlQELUFzrMsCmukrQNRISUpEGJuOuGUdbGFqPsbzZJM4D2DTIIFp\nj/ceDh2CRMJmIbuTcOBNWNuBRQUzOHsWLpyH1ekSLrW10HUSGi9AqM2++WWmUwLYH2slbUquggQX\nzrlNwAPAdu/9z9LbPgU87pz7He99z/THeO+H04/JfZ5PArudc6u896cLcaxSQqYnTC4fhRuT8Mx3\noLIHKpdBdBBGhuCGbdB6jY06VKfHamN90LwBAs2WiBlpsMTM0AX7ubIelt9m+zVsyRa/SoxqBYiU\nhUutLJnApjMyuRRxbGSitwdOn4bW3EDhCHSftXh8Ou/h4AFIJK3nYNxDMGD5HucOwa2tsMFlp0Bu\nQxU35WKFGrm4CxjIBBZpT2PTf3dgoxFXojH9mMH8Hp6UrMyHeybQeHSb/bzvh3A+Ds0RuGst3P9v\noCqcHXUAu73yVrjuLOz5HsQjEIxY1lsmMXPtDhg8kA0mtAJEylTuypIYNrWRyaFIAIeBSQ+HD0Is\nBb7eplQCIdtvz2G4fYWtxobstEr3EPQOQ7Aazo2B85CMQeMABA7Cls1wf2txKoNK+ShUcNEOnMvd\n4L1POef6ucIBZ+dcGPgj4Jve+9HL7S+LUEWV/cV87BNw7mEYGoe6AAR6oPFa2yd31CFz+0MfB2Kw\n+xR0d01NzJwpmFBgIWUqt2Pqe8hOmcSABuB0PySPQagKeiesZl1sAKrqoWfMBgHrG23UI7NahAa4\n/b3gk7AuYdsjk3DjzVCbXgGi/zFyOXMKLpxzXwQ+d4ldPLD5qo6It5M7v51+vk9c7fPJIrBsJSxL\n306tzAYEuYFC5naoCT76u/DQWLY7aW5ipoIJWYRyRxAywUayGe58n3VjzQQekw4CHkIhWN8wdSkq\nQMoBLVNHJTRCIXM115GLLwFfu8w+x4Eesh8FADjnKrAqsBflW0zbLxNYrAbuvdJRi8985jM0NDRM\n2bZz50527tx5JQ+XcjLbqMP02y1V6k4qS1YmEXTLumIfiZSKXbt2sWvXrinbhoaGCvJaznuf/ye1\nhM43gVtzEjrvB34ArJopoTO9Tyaw2ADc473vv4LX2gbs2bNnD9u2bcvXWxAREVn09u7dy/bt28EW\nYOzN1/NOX7WUF977Q8CTwFecc7c553YAfwHsyg0snHOHnHMPp29XYrUwtmHLVYPOueXpS/DiVxER\nEZFSVMg6Fx/Bimg9jdVc+Q7w6Wn7XIvlHQGsxApugZW1B5sO9MA9wE8LeKwiIiKSJwULLrz3g8xe\nMCuzT0XO7U6yOUUiIiJSpgoyLSIiIiJLl4ILERERySsFFyIiIpJXCi5EREQkrxRciIiISF4puBAR\nEZG8UnAhIiIieaXgQkRERPJKwYWIiIjklYILERERySsFFyIiIpJXCi5EREQkrxRciIiISF4puBAR\nEZG8UnAhIiIieaXgQkRERPJKwYWIiIjklYILERERySsFFyIiIpJXCi5EREQkrxRciIiISF4puBAR\nEZG8UnAhIiIieaXgQkRERPJKwYWIiIjklYILERERySsFFyIiIpJXCi5EREQkrxRciIiISF4puBAR\nEZG8UnAhIiIieaXgQkRERPJKwYWIiIjklYILERERySsFFyIiIpJXCi5EREQkrxRciIiISF4puBAR\nEZG8UnAhIiIieaXgQkRERPJKwcUStmvXrmIfQtnROZsfnbe50zmbH5230lCw4MI51+Sc+4Zzbsg5\nN+Cc+6pzruYyj/kD59xB59yoc67fOfevzrnbC3WMS53+E86dztn86LzNnc7Z/Oi8lYZCjlx8E9gM\n3Ad8AHg38OXLPOYw8NvADcAO4CTwlHOupXCHKSIiIvlUkODCObcJeAD4uPf+Ve/9C8CngF91zrXP\n9jjv/T9673/svT/pvT8I/CegHthaiOMUERGR/CvUyMVdwID3/mc5254GPHDHlTyBcy4I/HtgEHg9\n70coIiIiBVFZoOdtB87lbvDep5xz/en7ZuWc+wDwj0A1cBZ4n/e+/xIPqQI4ePDgVR3wUjQ0NMTe\nvXuLfRhlRedsfnTe5k7nbH503uYm57OzKp/P67z3V76zc18EPneJXTyWZ/FLwMe895unPb4X+H3v\n/ay5F865CNABtAL/DsvZuN17f2GW/T8CfOOK34SIiIhM92ve+2/m68nmGly0AJdLrjwO/DrwJe/9\n2/s65yqAKPBh7/135/CaR4C/9t7/8SWO6QEs+TN6pc8rIiIiVAHrgCe99335etI5TYukX/iyL+6c\nexFodM7dkpN3cR/ggN1zPMYAEL7MMeUt2hIREVliXsj3ExYkodN7fwh4EviKc+4259wO4C+AXd77\nnsx+zrlDzrmH07ernXNfcM7d4Zxb45zb5pz7G2AF8O1CHKeIiIjkX6ESOgE+AvwltkpkEvgO8Olp\n+1wLNKRvp4BNwMewfIs+4BXg7vSyVBERESkDc8q5EBEREbkc9RYRERGRvFJwISIiInlVlsGFmqLN\n3VzPmXOu0jn3x865N9Ln7Ixz7uvOuY6FPO5im+fv2iPOuSedcxecc5POuUVfvt4599vOuRPOuQnn\n3EvOudsus/97nXN7nHNR59wR59xjC3WspWIu58w5157+PTzsnEs55/5kIY+1lMzxvD3inHvKOXcu\n/X/4Befc/Qt5vKVgjudsh3PuufTfr/H05+Z/nOtrlmVwgZqizcdcz1k1cDPweeAW4BHgeuCKa5Qs\nEvP5XasBngU+ixWWW9Scc78C/A/gD7DfldeBJ51zrbPsvw74v8CPgJuAPwO+6px730IcbymY6znD\nluOfA/4QeG1BDrIEzeO8vRt4CngQ2AY8A3zfOXfTAhxuSZjHORvDVne+C1tk8YfAf3fO/ds5vbD3\nvqwu6Tc7CdySs+0BIAm0z+F56tLPc0+x31MZnbNbsVU9q4r9nsrhvAFr04/fWuz3UuDz9BLwZzk/\nO+A08NlZ9v9j4I1p23YBPyj2eynVczbtsc8Af1Ls91Bu5y3nMfuB3y32eymzc/bPwNfn8rrlOHKh\npmhzd9XnLK0x/ZjBPB5bKcvXeVu00v+XtmOjEAB4+2v0NHb+ZnJn+v5cT15i/0VlnudsycvHeXPO\nOeyL5aX6VS0aeTpnt6T3/clcXrscg4sZm6JhvyyXbYrmnBvByoR/mss3RVss5n3OMpxzYeCPgG96\n70fzfoSl6arP2xLQClQAvdO29zL7OWqfZf/69O/ZYjefcyb5OW//GZu2/FYej6uUzfucOedOOeei\nwMvA//Tef20uL1wywYVz7ovp5LfZLinn3HVX+TI/xuZ47wJ+CHz7EvNOJW+BzhnOuUqsSqoHPnHV\nB15kC3XeRKR0OGty+XvAL/tZGmHKFHdjox6/BXwmnbtxxQpZoXOuvgRcLjI6DvQAy3I3OmuK1py+\nb1be+4n0cxwHXnbWFO3j2BxwOSr4OcsJLFYD9y6SUYuCn7cl5AKWh7N82vblzH6OembZf9h7H8vv\n4ZWk+ZwzuYrz5pz7VeB/Y40znynM4ZWkeZ8z731n+uabzrl24L8C/3SlL1wywYUvwaZopa7Q5ywn\nsNiAJb4OXP1RF98C/64t6tUi3vuEc24Pdl6+B2/Pa98H/PksD3sRy97PdX96+6I3z3O25M33vDnn\ndgJfBX7Fe//DhTjWUpHH37UK5vpZWexM1nlmv/4AeBW4DVtWehj4+2n7HAIeTt+uBr6AJeGtwZYk\n/Q0wDmwu9vsp0XNWiS077QRuxCLdzCVY7PdTquct/XMTNv32fmy1yKPpn5cX+/0U6Bw9mv6/9DFs\nhc2XseCtLX3/F8nJNMfaO49gI4bXY1NtceDniv1eSvWcpbfdhC0PfwX4+/TPS+Lv11X8rn0k/bv1\nW9P+htUX+72U8Dn7BPAQcE368nFgCPj8nF632G98nierEfiH9BseAL4CVE/bJwV8LH07jC2lOQVM\nYMtw/gXYVuz3UsLnbG3659zLZPr63cV+P6V63tI/P5ZzrnIvv1/s91PA8/QJrHbMBDYCcWvOfV8D\nfjxt/3cDe9L7vwX8erHfQxmcs5l+p44X+32U8nnDlu1OP2cp4G+K/T5K+Jx9EtiHfQEYwL5c/eZc\nX1ONy0RERCSvSma1iIiIiCwOCi5EREQkrxRciIiISF4puBAREZG8UnAhIiIieaXgQkRERPJKwYWI\niIjklYILERERySsFFyIiIpJXCi5EREQkrxRciIiISF79f3QrkHKpK0KQAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10cc0a400>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "from sklearn.datasets import make_moons\n",
    "\n",
    "X2, y2 = make_moons(n_samples=200, random_state=5)\n",
    "X2_kpca = kpca.transform(X2)\n",
    "\n",
    "plt.scatter(X_kpca[y==0, 0], X_kpca[y==0, 1], \n",
    "            color='red', marker='o', alpha=0.5, label='fit data')\n",
    "plt.scatter(X_kpca[y==1, 0], X_kpca[y==1, 1], \n",
    "            color='blue', marker='^', alpha=0.5, label='fit data')\n",
    "\n",
    "plt.scatter(X2_kpca[y2==0, 0], X2_kpca[y2==0, 1], \n",
    "            color='orange', marker='v', \n",
    "            alpha=0.2, label='new data')\n",
    "plt.scatter(X2_kpca[y2==1, 0], X2_kpca[y2==1, 1], \n",
    "            color='cyan', marker='s', \n",
    "            alpha=0.2, label='new data')\n",
    "\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example 2 - Concentric circles"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Following the concepts explained in example 1, let's have a look at another classic case: 2 concentric circles with random noise produced by scikit-learn’s `make_circles`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAscAAAIiCAYAAAAkf2UfAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nqXcjfOTq9gAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10c9458d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sklearn.datasets import make_circles\n",
    "\n",
    "X, y = make_circles(n_samples=1000, random_state=123, \n",
    "                    noise=0.1, factor=0.2)\n",
    "\n",
    "plt.figure(figsize=(8,6))\n",
    "\n",
    "plt.scatter(X[y==0, 0], X[y==0, 1], color='red', alpha=0.5)\n",
    "plt.scatter(X[y==1, 0], X[y==1, 1], color='blue', alpha=0.5)\n",
    "plt.title('Concentric circles')\n",
    "plt.ylabel('y coordinate')\n",
    "plt.xlabel('x coordinate')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from mlxtend.data import iris_data\n",
    "from mlxtend.preprocessing import standardize\n",
    "from mlxtend.feature_extraction import RBFKernelPCA as KPCA\n",
    "\n",
    "kpca = KPCA(gamma=15.0, n_components=2)\n",
    "kpca.fit(X)\n",
    "X_kpca = kpca.X_projected_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAjkAAAGHCAYAAABSw0P1AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nFEVRFKUoUZGjKIqiKEpR8v8AQNf52EM8Fg0AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10e1a9208>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(X_kpca[y==0, 0], X_kpca[y==0, 1], \n",
    "            color='red', marker='o', alpha=0.5)\n",
    "plt.scatter(X_kpca[y==1, 0], X_kpca[y==1, 1], \n",
    "            color='blue', marker='^', alpha=0.5)\n",
    "\n",
    "plt.title('First 2 principal components after RBF Kernel PCA')\n",
    "plt.xlabel('PC1')\n",
    "plt.ylabel('PC2')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAgkAAAGHCAYAAAA6MMHNAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\nAAAPYQAAD2EBqD+naQAAIABJREFUeJzt3XmcJWV97/HPb/ZhGVZZFYRhNUEjY4wGNQoi4i4ajAFj\nNGqMelU0SuKNG+o1Xnm53rhEr3oFwauiV0HZBBU0AeKMisogw8gmmywDw8wwCzPP/eNXZVefebqn\ne6ZPn4b5vF+v8+ruOs956qnn1Kn61lNVp6OUgiRJUq9pg26AJEmamgwJkiSpypAgSZKqDAmSJKnK\nkCBJkqoMCZIkqcqQIEmSqgwJkiSpypAgSZKqDAlbICJ+FxH/Puh2bImIeH9ErOtj/UdFxIaI+PM+\nzmN6M4939GseGpyImBERp0bETRGxPiK+Nug2aWJFxOkRsWTQ7dDGDAkVEfHyZqdTe/yPTtENwIR9\nr3VEnBAR/22i6hujQi5Hv+ehh7iIeH1EvKwPVb8GeAtwJvA3wMcjYtuIeHdEPKkP86uKiPk924L1\nEXFXRJwTEY+vlH9fpfzNEfHt3vKVuruPSzbRrr9ryj26Z/qOEbEwIlZGxFET0wt9UxjDdiIiftzT\nN3dFxOXNNjsq5Y+MiG9FxK0RsSYibm/6//kj1H9YU+/KiNhuApbrQW/GoBswhRXgncD1PdN/1fl9\nPrB+Aud5YlPnJyewzk15N3BKvyovpVwUEXNLKWv7NQ9NGW8AbgJOm+B6nwZcX0p5ezshInYn1911\nwI8neH6bchpwPjAdOBh4PXBxRDyulHJ1T9lChpz7yYOyfYC/B37UlP/1CHV3/X4MbRq2g42IHYDv\nA4cAzyulXDSGOh4MCnAD8A4ggIcBfwt8kdx2vqstGBEfAP4Z+A3waeBGYFfg2cA3I+IlpZRv9NR/\nAnBzU+444Mt9XJYHBUPC6M4rpSwa6clSyiaH6SNim1LKqolt1pZr21VK2UCfRxIMCNpCuwH39Ezb\n6KhxIozx87qwlHJG5zX/CZwNvBZ4c6X810spyzvlzwF+DrwY6A0Jw+reHBExD7gQeBQTGBCm0LZs\nWSnlzPaPiPg8GQTeGBHvLqWUiPgrMiCcCfxNKaV7MHdqRDxzhLpfCpwOHEoGhq0+JHi6YQv0XpMQ\nEa9qhqqOiIjPRMTvgeua5+ZFxCci4vqIWN0Me50fEYc1z18KHAMc0BlKu2aUebfn4T8SES+LiN9E\nxP0RcUXv+f/muoMNEXFQRPzfiFgG/KDz3LoR6j0uIn7VtPeXEfH0SjseHhFfiIhbmvkvjYj/FRHT\nmuc3uiahGTJcFBGPi4j/iIhVzete3VP37GbIdmFE3BMRKyLihxHx5PG8Tz11zomIUyLimma5bomI\nr0fEvp0y20XERyPPga+OiMUR8eaeerr9dHxEXNUsx08i4lFNmddFxLVNv1wUEQ/vqWNM/dCU3a3p\n59ub+n4WESf2lGmHrN8YEX/f1HV/RFwWEY+t1HloRJwVOWS7qll3ntVTpl2n/ywiPhYRdzTvwzci\nYudOuZuAg4Cnd9bfCzbxXpzc9Fc7//+KiBf0Lg/wJOBPYmjI/gjgFvKo8v2d+b2j89rxLNtGn9dx\nurT5OX+M5W9vfj6wGfMaVURsD1wA/DHwglLK9ytltqhvYmh78siI+HLz2VwWEZ+LiNmV+b08In7a\nzOuuiPhKROw1UctcSlkJXAFsD+zSTD6FHIF5VU9AaF9zXinlvJ52PhV4OPBV4P8CR0aOWG3VHEkY\n3Q4RsUt3Qinlru6fPeXbvz8L3Aa8B5jTTPsc8FzyVMLV5HDWk8jE+kvgvcCp5FHTW8kjpfvG0Maj\ngL8GPkEOvb4eOD9yKPM3Pe36ZjPvk3vaXDsX+FTgL4FPASvII6SzImKfUsq9ABGxN/BfwHbAZ8g0\n/4jmdXOA9qij1k+7AueQSf8rwF8Bn42I+0sppzfldiSHEs8k+3Qe8CrggqgP1Y4qIqYD5wJPaeb5\nkabOZ5BHXTdERADfBY4g37MrgWOBj0TEnqWUk3uqfRrwAnI4cxp59HJ2RHysaesnyQ3XycDnge4R\nzJj6ISK2AS4B9m3quwE4HvhyRGxfSvl0T5teDmxDvnfRzPusiDigGTkiMpxe2tT1QfK9egnwnYh4\nQSnlnE4baeq6kxzO3Z9cH+4H2msQ3tCUuaupL4BbN3oThnsjcBZ55DaLXI/PiohjSykXkJ+hE5t5\nzmZoiPl6cj3/N+DrwLeb+n6+mcvW/bzO3USba/Zrfi4b4fldImImuX48olmeVU3be23bu80B7qnt\n6CrmAecBjwFe2PThMBPUN+024yzgWnL9ehzwyqbsOzvze3ezvGeQn6fdgDcBj4+Ix5ZSVoxhucZi\nPhm6lkfEIcABwGdKKfePo44TgN+UUn4ReRHlGvLz+PEJauODUynFR8+D3MhuqDzW95S7Cfj3zt9/\n15S7qFLncuAjm5jvucA1Y2zj9GZeDwB/3Jm+L7Aa+Gpn2vuasl+q1PM+YG2l3lXAPp3pj22mv6Yz\n7SvAWuDRo7TzKPK6jT/vTLu0mfb6zrRZwC+A3wHRTJsGzOipbwfyCOHTlTa/YxN99uqm3OtGKfOi\npsw/9kw/iwxh+/TMcyWwV6fcPzTTbwLmdqZ/qFnmvTajH97alHtxzzJfTu6Y5jbT5jfzvg3YrlP2\nhc3rn9GZ9kPgp8D0nuW8DPhVZZ3+bk+5jzfv/TadaYuBC8bxOZvd8/cMcvj93J7plwKLeqbtPtJ7\nvhnLttHndYT2tv37z2Tw2w14cjOv9cBzK5+t2nbkTuDIEepe31N22GdnhHa1y3EdGdyOHaXsFvdN\nZ7k+1TP928Atnb/3J7dPb+0pdxj5WfrHzrTTGMO2r1kXftH0/y7kNRefbNrz9c76PurnvFLvLOBu\n4J2daV8FrhhrHQ/Vh6cbRlbIDf7TO4+jx/i62m2R9wJPiIg9JqyF6dJSyh8upiyl3ECeH+0951bI\no/2xOq+UcmOn3p+RO8T94Q9H5c8DvlVKuXIz2r2GPLJu619L9tueZCChlLKhlPJAM7+IiJ2AmeRG\n7vDNmOdx5A6098i761hy5/dvPdM/Qu6Ye/v1/FLKLZ2/L29+fq0MP4ppp+/f8/pN9kPTpptL5yKr\nkkeWnyCPHntPv5xRhh+hXUoegbfv3a7kaMrXgB0jYpfmsSt50dyhEfGwzusLeURJT53TyQvxNksp\nZU37e0TsSI4c/ZjNe2/bejZn2cZ7G/P7gTvIdelH5FHrm0opZ1fKFvJz0m4//hZYCnwrIv60Uv7T\nbLzN+eUY27UbeYDwu9qTE9w3I60Tu0dEO3r6oqbcWZ157UKOMP2WHIXbHIeR/X8HcBW5nf42eYEo\n5GeiMLaR2NZzyAOQMzvTzgQWRMSBm9nOhwRPN4zuv8ooFy6O4vrKtLcBXwB+FxE/Bb4HfLmUUis7\nHtdWpl0DHBcRO5dS7u5MH8/51psq0+4Bdmp+3x3Ylo0vvBqrm7s7icY15M7skcAigIh4BXn728EM\nX19HvF5jFPOBq0tzmDCCfYHflY2HKRd3nu/q7ad7m5+9G+p7yWXbqWf6WPphX+rLu7gpt6k2tcPg\n7bzbjd4HgX+t1FvIHc4d46hz3CLieeQphMeQpxNaW3Kh6+Ys2/XjnMenyVN3c8mRsjeQgWkkl5Th\nFy5+kwwKnwCe2FP2mlLKxeNsD+RyvZo8qr4gIp5USlnaU2ai++bGnr+768StZHiaTgaC2ryWV6aP\nxbXkHSKQoeiaMvw08HLyc7H9OOo8sam3RER7bcm1ZIg/gTzdslUyJPTHRufBSilfjYgfkUNhR5Oh\n4eSIeH6pXFw0We0axUjnQPtyVXl1RhF/C/xv4Bvkhu0Osl3vBPaerHZswkj9NMj+29S82xHED5G3\nydX0BsoJXZ6IeBrwLeBi8q6A28gh6FeTR6Cba3OWbTyfCxi+I/9uXsbCqRHxw1LKLzb14lLKioi4\nAjg2ImaVibv751fAs8jlvjAijiildK8Lmei+Gct69gAbj761xnOk37WilPKDUZ5vb0M9bCyVRd4u\neix5yqH3C50Kea3Me8bZxocMQ8Ikaj6wnwI+1Qzr/YI8kmo/sJvzpUO1obCDgft6RhEm2u3k6Yc/\n3szX7x0Rs3uOog8m++D65u8XkRcSHd99YQz/QqvxWAo8JiKmleYCvoobgCdHfrdDdwN5aOf5iTRa\nP7Qb7Buov8+HMnTf+Hi0R5hrN/OodSTjWX+PI9efZ5bORXkR8fcjv2RM8+rXso3mfeQ5/PeRpxbG\nYga5M92WLRs5GaaUcnlEHEeecrwwIp5cSmmP8Ce7b5bSjCRMwIjpmJVSFkfEtcALI+ItlVHBXn9J\nBoRXs/GttocCp0TE40spV/ShuVOe1yRMgsjb5YYNfZVS7iCH5LrDrCvJ87Lj8aTofNNaRDySPL92\n3kgvmAjNhv3bwAsi4jGbUcVshs4hEhGzmr9vo7lKncqRSuTtb7VzuWNxFrAHeQ5zJN8jNxiv65l+\nUtOeczdz3lDfsY3WD+1R6feAh0fEizrlZgD/jRxavZRxKKXcRp77/4eI2K33+eYc9eYYz/rbXqD3\nh2H6iNifvANorPOid359XLYRNTvhzwHPjog/2lT5pg1PIE9rjXRHxJa050Jy+PwQ4Nzm7phB9M1Z\n5Dr/7tqT0bmFtg/eQ546+ffm+qneeR8TQ9+VcCI5OvSFUso3uw/yjrP7yVMOWyVHEka2ucPCtdft\nCFwXEV8nL0JaSd529yfkbWCtheS1BB9ufl9eSvneJub3a/Ic5CfJob3XNT/fu5ntH49/Ao4EfhwR\nnyVvgdybTOZ/Woa+eKXWJzcD/705/3ct+SUmfwS8onOUfw7wvOYc7rnkNQV/T16stNH92GPwRfKW\nvU9ExBOBn5C3bx4NfLSUci45BH4J8KGIOIChWyCfDXy4lFK7VmOsNrcfPkMe5ZwWEX9Gjhy8hAxL\nbxjDkVLNP5DL+auI+Bw5arE7eevnbuQtbaO1uzZ9IfB3kd9XsBS4rZTyoxFe+11y3T8/Is4kL9R8\nHbkObXJHW0pZGfk9Ii+NiN+S58OvLKUsnqBlG6+PNctzMvnV0d36XxIRq5rfH06OOswjg+dEGbYc\npZRvRMRryQsPvxMRz2pOa0xa35RSljS3QJ7SrN/fIW+n3p887fpJ8rqMCVdKOaM5eHob8LhmHbuR\nvCPiWPKiyeMjv7vkycCHR6hnTURcSL6HJ40yAvmQZUgY2ViGTmvfMVB73X3kxU7PIIfQg9whvKaU\n8r875f4XeR7tleTFekvJo8jRXERe3PYucgP0S+ClzcZyrGrLUFuOYdNLKb9rdlrvJ9P4PHKn913y\ngqKR6oe8Day90OrV5JHza0spf/iGs1LK55sjnleTXzR1FXnf8olA73flj9TmoQKlrI+IY4B/IXfG\nL27acSnNBZillBIRzyaHjo8HXkGe/nhLKaX3fukx9VPP9F5j6YdVEfEU8mKzl5P9fDXwsrLxt/ON\n9b37dUQ8jjziegV5sdnvgZ+Ry76pdtemv4dcB08mw9dF5NX/G7+wlAsjvzTq7eQO9rfkrZ4HUw8J\ntTa8krwV86Pk6M87gcUTtGwjqfZv81n4Krkz+ZfOnUG9dxWtJEfK3lZK+X9jqXsc7ept0+ebo/UP\nAl+NiBf3uW82blQpH4iIxeT3arRfmXwTuY04p7f4WKsd47z/qdnBv4EMoDuRpxMuB55fSjknIt7W\nFO9tS9fZ5GmkZ9DnEdqpqL0PWw8yzRDaOuBjpZS3DLo94xH57ZLbllI2+1a3hwL7QdJU5zUJkiSp\nypAgSZKqDAkPbltyDnPQHqztnmj2g6Qpy2sSJElSlSMJkiSpamC3QDb/6OMY8vay1aOXliRJHXPI\n/+9yfs//rphQg/yehGPIfzUsSZI2zwlA7/elTJhBhoTrAU4//XQOPfTQTRR96DvppJP46Ec/Ouhm\nDJz9MMS+SPZDsh+G2BewePFiTjzxRBj/fzEdl0GGhNUAhx56KIcf7nfJ7LDDDvYD9kOXfZHsh2Q/\nDLEvhunr6XovXJQkSVWGBEmSVGVIkCRJVYaEKeKlL33poJswJdgPQ+yLZD8k+2GIfTF5BvaNixFx\nOLBw4cKFXoAiSdI4LFq0iAULFgAsKKUs6td8HEmQJElVhgRJklRlSJAkSVWGBEmSVGVIkCRJVYYE\nSZJUZUiQJElVhgRJklRlSJAkSVWGBEmSVGVIkCRJVYYESZJUZUiQJElVhgRJklRlSJAkSVWGBEmS\nVGVIkCRJVYYESZJUZUiQJElVhgRJklRlSJAkSVWGBEmSVGVIkCRJVYYESZJUZUiQJElVhgRJklRl\nSJAkSVWGBEmSVGVIkCRJVYYESZJUZUiQJElVhgRJklRlSJAkSVWGBEmSVGVIkCRJVYYESZJUZUiQ\nJElVhgRJklRlSJAkSVWGBEmSVGVIkCRJVYYESZJUZUiQJElVhgRJklRlSJAkSVWGBEmSVGVIkCRJ\nVYYESZJUZUiQJElVhgRJklRlSJAkSVWGBEmSVGVIkCRJVYYESZJUZUiQJElVhgRJklRlSJAkSVWG\nBEmSVGVIkCRJVYYESZJUZUiQJElVhgRJklRlSJAkSVWGBEmSVGVIkCRJVYYESZJUZUiQJElVhgRJ\nklRlSJAkSVWGBEmSVGVIkCRJVYYESZJUZUiQJElVhgRJklRlSJAkSVWGBEmSVGVIkCRJVYYESZJU\nZUiQJElVhgRJklRlSJAkSVWGBEmSVGVIkCRJVYYESZJUZUiQJElVhgRJklRlSJAkSVWGBEmSVGVI\nkCRJVYYESZJUZUiQJElVhgRJklRlSJAkSVWGBEmSVGVIkCRJVYYESZJUZUiQJElVhgRJklRlSJAk\nSVWGBEmSVGVIkCRJVYYESZJUZUiQJElVhgRJklRlSJAkSVWGBEmSVGVIkCRJVYYESZJUZUiQJElV\nhgRJklRlSJAkSVWGBEmSVGVIkCRJVYYESZJUZUiQJElVhgRJklRlSJAkSVWGBEmSVGVIkCRJVYYE\nSZJUZUiQJElVhgRJklRlSJAkSVWGBEmSVGVIkCRJVYYESZJUZUiQJElVhgRJklRlSJAkSVWGBEmS\nVGVIkCRJVYYESZJUZUiQJElVhgRJklRlSJAkSVWGBEmSVGVIkCRJVYYESZJUZUiQJElVhgRJklRl\nSJAkSVWGBEmSVGVIkCRJVTMG3QANwIUXwotfDMuXj/01ETBvHuyyC+y4I5QCa9bAdtvBAQfA0UfD\nEUfAsmVw772www4wf36WfxC4666Nm1qbNtpzS5bAgQcOf37JEth55+HlRppPt8677hp6/u67s94L\nL4RHPjKn7bxzTm/rbud1/fVw+OH5XPtWHH748DIHHpg/ly2DnXbKOtr5L12aZdvp7fy7li3Lt7Y7\n/6VL4fGPz9/bdrb1t+3tLuNZZ+X0efPyZ3e5li6Fm26CRzxiqC3XXz80/7bu9rne9rTLMH8+nH02\nPOpRWe7KK+FFL8r2Qa7+8+bBzTdnmba+K6+ERz8azj8fDj44px99NFxxRT723BOe+tSNl/nmm+G5\nz83p7Ufg8Y/PZV60KNvdvm/nn58fnUc9amhZr7oqX//DHw618/DD4fOfh6c9Ldv2k5/A3nvn9KVL\nsz3HHDPUPzvskPXsvXe2+UtfGvpYtm1p143587OOtu+67+3SpUPvXfd9bN+js8/OtnZf113mJUuG\nv7Zd53rXqdpn44orhr+f3fWvXY80eQwJW5Nrr82ty333jf+1peRW4N57N37uiivgjDMySMyZA9On\nw9y5cMgh8LKXwYkn5t9T1FVXwRe+AK985dDOojZttPLf+Q6ccgq8612Zmb7whdwpfOYzsPvuQzvD\nHXeEt71t4/k85SlwySVZJ8CHPwz33JM7sttvh0MPzXlssw1svz3stRfceSfsuy/ssw8sWAAf+EBO\n22+/fIvvvhvWr895LViQjy99KXcqp52WO4x58+AJT4BXvAI+/nG47DLYsCHb2bZxyRJYty5/X7cu\ns+F++8GqVTn/FSty1Xrve+HWW+HUU2H27Jz33LnZ5gULch6XXAI33ADf+MZQf06blu3Yfvuc729+\nA2vXwowZ+Zg5E1auzHZF5M61bU87n7Y922wzFBK22Sb7Y8YMmDUL7r8fHvMY+OUv8zVd06fnfKZN\ny3LTp8MDD+RzM2bAkUfCD34wNN8998x+aJf5X/8127frrtkfa9fmR+HNb4bvfx9+9rNcxgMOyPmv\nWpX1RORHq/25/fb53GGHweLFOe+VK7Nds2bB6tVZ9hGPgFtuyTbOnJnL09azYUOWP+gguPrqbMfs\n2fD61+f6dtll2cY994Tf/z7Xn3vuyfmuWZPTb701X1dK9sfcuTmfmTNznrfemuVmzMjnly/P6XPm\nwAknwMUXZ53335879Ze9DL797fwstOsUZHjofjb22gs++9n8uWpV9uctt2S/z5w5tJ73fibVP1FK\nGcyMIw4HFi5cuJDD20Md9dchh+QWuN+23Ta3srNm5RbojW+El7+8//PdDKXAxz4G3/sePOtZuVGH\njadFjFy+FHjhC+HSS+FJT4K/+It8/vbb4be/HcpOEXkk9NrXwkknDc3nu9/NLlu5MussJTeUd9+d\nG9nuDhpyBzBt2tBOeK+9cmN99dUjL+f8+bmjuOWWfFt+//uh53bZJYPCxRfn/Fpz52abV6/OHU9X\nxNBbvHZttuXAA3PH0K27LbvTTnlEu2JF9lO7A+41bdrG8xqLtj0bNmze6zfXQQfl0fIdd9Sf3223\nfB+7gWOkZe+33XbLdagdhZkIbbjpmjMn14nu+7DbbhlcI3JdWbs2p8+dO/TZ2GGH/Ax0158ZM7J8\nW9fOO8M73gFvecvQZ3JrtWjRIhYsWACwoJSyqF/zcSRha3HhhZMTECC3gtttlz/vuw8uugie85wp\nOU541VWwcGFmmYUL8+itlI2ndY/8e59bsiSHqHfdNactX54bt/aIds2a3DjPmJEbxR/8AJ75zKH5\nzJuXR5qPfWzuqFesyJ31ihX5unbD2uruCFevzqPlTQ0O3Xprvma77TbeoS1fnkPc3YAAG//dVUq+\nve0Ob/r0HE2o7aBLyfZdfnku/2g7yc3dwbftmWxLl248KtHVG5gGFRAg2zJ9+sTWWTvGXL26Pu9Z\ns3L5u+9xG4Lb8NSux229bTBurVyZpzqOPdbRhMliSNhaLFw4efNav34o5m/YkIcud9895UJCKXDB\nBblRO+AA+NWv4Lzz8rnutPPPz+F+2Lj8uefmEPq6dRkcfv7zPKLfYYec1h4Zt0Pla9fCjTfm6yJy\nI7lyZZZdsSJHH+64Y2gHvKmdZil59L4pq1blDmLlyo037OvWbbwxHq8NG+o7jO48ukfUDxWjBYSp\naJDtXbdu43WkDXcbNmSY3tT6vnZtfr7OPTc/k1v7aMJkMCRsLXJYanJMnz60NZg2bfhVcFNIOyrQ\nXiD3iEfkkXxEhoB2Wu8IQ7f82WfnSMJuu+WOeNq0oUs3pk0bvlPcsCE3csuX5+u23z67ZskSeNjD\n8uKzVauGLvsYy1H1eM4Wrl8/+ujAlhhLOx5qAUHjM9I6UsqmQ2a3bPv5cTRhcngL5Nbi6KOHLtXu\nt/ZqpojcEx511JQdRVi5MofA2wvNbrghd9btedW5c7PMeefliEK3/OzZeVRz3335+x13ZL1r1+ZR\nUXsxWeuBB3IUYsWKfN111+UV8atX5/yWLctRgbVrs/sGdLmQNOnGs66vXp2h/dxz/YxMBkcStibn\nnLP5dzeMRfcKvdmzh+5uOP74/sxvC9x2W+6k58zJn5A75jVr8vfFi4duyJgzB37966Hf2/LLluUG\nq5QMFu1pg3YEoLYBW7s2y82YkW/DqlUZJm66KX9vL/hy4yfVlZKfoZ/+ND/He+456BY9tBkStiYH\nHJBjdX5PAnvskXcYtFdZQy7SzTfn73vvPfx858yZ+bN77n7Dhjz98MADebrh9tuzviVLckRgu+2y\nO1asyLsXZs7MLtljj/x9jz1yHu252vZ6hHXrckRjxoy8Xe7OO4fCywMP5GmMiLydbPr07O72CvBV\nq3J+69fn69vby+bOzTbMnp1hqA0ys2fntQLdWw5hKLxMm5Zl1q3Lv9t6Z83K37fdNttx551D11Ws\nX5/tai+63HHHfKxcmbddtmGse81F29e9dym0ozHtMnfLzZiRbeue3ZoxI4Nbe8dFey1IKcOD1+Ze\nIDltWs6jrbO9w6Ptm/aUyqxZWa6UoQtW77kn2zbSdQHt8rWnqdq/t6St7d3I7Xs4b95Qhl+5cug9\nmDUr35N2fr393t6KCbnutqcIuncpdPu4XffmzBm6fXHatPx75sycNmtWTps7d6jM6tXZprVrh27J\nnD07b2fdeeesc7/98lbWI47Iz5D6y5CwNTr66Pr3HWxFInJj0+uQQ8ZXT3tBoyQ9FHlNgiRJqjIk\nSJKkKkOCJEmqMiRIkqQqQ4IkSaoyJEiSpCpDgiRJqjIkSJKkKkOCJEmqMiRIkqQqQ4IkSaoyJEiS\npCpDgiRJqjIkSJKkKkOCJEmqMiRIkqQqQ4IkSaoyJEiSpCpDgiRJqjIkSJKkKkOCJEmqMiRIkqQq\nQ4IkSaoyJEiSpCpDgiRJqjIkSJKkKkOCJEmqMiRIkqQqQ4IkSaoyJEiSpCpDgiRJqjIkSJKkKkOC\nJEmqMiRIkqQqQ4IkSaoyJEiSpCpDgiRJqjIkSJKkKkOCJEmqMiRIkqQqQ4IkSaoyJEiSpCpDgiRJ\nqjIkSJKkKkOCJEmqMiRIkqQqQ4IkSaoyJEiSpCpDgiRJqjIkSJKkKkOCJEmqMiRIkqQqQ4IkSaoy\nJEiSpCpDgiRJqjIkSJKkKkOCJEmqMiRIkqQqQ4IkSaoyJEiSpCpDgiRJqjIkSJKkKkOCJEmqMiRI\nkqQqQ4IkSaoyJEiSpCpDgiRJqjIkSJKkKkOCJEmqMiRIkqQqQ4IkSaoyJEiSpCpDgiRJqjIkSJKk\nKkOCJEmqMiRIkqQqQ4IkSaoyJEiSpCpDgiRJqjIkSJKkKkOCJEmqMiRIkqQqQ4IkSaoyJEiSpCpD\ngiRJqjJExKf8AAALIUlEQVQkSJKkKkOCJEmqMiRIkqQqQ4IkSaoyJEiSpCpDgiRJqjIkSJKkKkOC\nJEmqMiRIkqQqQ4IkSaoyJEiSpCpDgiRJqjIkSJKkKkOCJEmqMiRIkqQqQ4IkSaoyJEiSpCpDgiRJ\nqjIkSJKkKkOCJEmqMiRIkqQqQ4IkSaoyJEiSpCpDgiRJqjIkSJKkKkOCJEmqMiRIkqQqQ4IkSaoy\nJEiSpCpDgiRJqjIkSJKkKkOCJEmqMiRIkqQqQ4IkSaoyJEiSpCpDgiRJqjIkSJKkKkOCJEmqMiRI\nkqQqQ4IkSaoyJEiSpCpDgiRJqjIkSJKkKkOCJEmqMiRIkqQqQ4IkSaoyJEiSpCpDgiRJqjIkSJKk\nKkOCJEmqMiRIkqQqQ4IkSaoyJEiSpCpDgiRJqjIkSJKkKkOCJEmqMiRIkqQqQ4IkSaoyJEwRZ555\n5qCbMCXYD0Psi2Q/JPthiH0xeQwJU4QrfbIfhtgXyX5I9sMQ+2LyGBIkSVKVIUGSJFUZEiRJUtWM\nAc57DsDixYsH2ISp495772XRokWDbsbA2Q9D7ItkPyT7YYh9MWzfOaef84lSSj/rH3nGEX8NfGUg\nM5ck6aHhhFLKGf2qfJAhYRfgGOB6YPVAGiFJ0oPTHOCRwPmllLv6NZOBhQRJkjS1eeGiJEmqMiRI\nkqQqQ4IkSaoyJEiSpKq+hYSI2CkivhIR90bEsoj4fERsO4bXnRIRt0TEqoi4MCIOqJR5YkRcFBEr\nmvp/GBGz+7MkW66ffdEpe25EbIiI501s6ydOP/qhqfMTEXF18/wNEfHxiJjX36UZn4h4fURcFxH3\nR8RlEfGnmyj/1IhYGBGrI+KaiHh5pcxfRsTips5fRMSx/VuCiTHR/RARr4qISyLi7uZx4abqnCr6\nsU50yv5Vsz345sS3fGL16bOxQ0T8W7PdWN1sH57Zv6WYGH3qizd3to83RsRHxrW/LKX05QGcCywC\nHgf8OXANcPomXnMycDfwHOCPgf8HLAVmdco8EbgHeBtwCHAg8GJgZr+WZar2RafsScA5wHrgeYNe\n3snsB+CPgK8DzwL2A54K/Ab42qCXt7MMLyFv8/2bZp39bLNMu45Q/pHACuB/AgcDrwfWAUd3yvx5\nM+0tTZlTgDXAowa9vJPcD6cBrwUeDRwEfAFYBuw56OWd7L7oKXsT8EPgm4Ne1gGsEzOB/wLOBp4A\n7AM8GThs0Ms7gL74a+D+pu59gKcDvwNOHXO7+rSwhwAbgMd2ph0DPADsMcrrbgFO6vw9r1nA4zvT\n/hN4z6Df0KnQF830PwFuBHZr5jMlQ0K/+6HnNS9uykwb9HI37bkM+Hjn72g+qG8fofyHgCt7pp0J\nfK/z91eB7/SU+U/gU4Ne3snsh8prpgH3AicOenkH0RfN8v8YeAXwRaZ+SOjHZ+O1wBJg+qCXbwr0\nxSeBC3vKnApcMtZ29et0wxOBZaWUn3WmfR8owJ/VXhAR+wF7ABe100opy4HLm/qIiIc1r78zIn4S\nEbc1pxqO6M9iTIi+9EVTbi75rZWvK6X8fuKbPqH61g8VOwLLSykbtrTRWyoiZgILGL4MhVz2kZbh\nCc3zXef3lH/iGMpMGX3sh17bkkeSd292Y/usz33xbuD2UsoXJ6a1/dPHfnguTWBu9hG/jIh/jogp\new1eH/viP4AF7WmLiNifHHX97ljb1q9O2wMYttMqpawnP7h7jPKaAtzeM/32zmv2b36+mxyKOYYc\nvr4oIuZvebP7ol99AfBR4MellHMmpql91c9++IOI2BX4F3L9mAp2BaYzjmVoptfKz+ucSxypzEh1\nDlq/+qHXh4Cb2XjjOZX0pS8i4knkCMKrJq6pfdWvdWJ/4C/J/dux5Km4twL/fQLa3C996YtSypnk\n/vLHEbGWHGH5QSnlQ2Nt2LhCQkR8sLkYZqTH+og4aDx1jlPb3s+UUr5cSvlFKeUt5DnoV/ZxvhsZ\ndF9EXqB4JHk9wsAMuh962rI9mZB/Bbx3MuapqSMi/gk4HnhBKWXtoNszmSJiO+DLwKtLKcsG3Z4B\nm0buLF9TSvlZKeXrwAfI0xBblYh4KvAOctkfCxwHPCci/mWsdYz3v0CeSp7nGs1vgdvIc+R/EBHT\ngZ2b52puI8/B7M7wdLQ70A5R39r87P3XkYvJizIm06D74mlkYr43Irqv/WZEXFJKOXIMyzARBt0P\nbV3bkUNt9wDHNaMUU8Gd5AWlu/dM353Rl7tWfnkpZc0myoxU56D1qx8AiIh/BN4OHFVK+fWWN7ev\nJrwvIuIQYF/g7BjaIEwDaI4gDy6lXDcRjZ9A/VonbgXWNsP1rcXAHhExo5TywJY1uy/61RenAKd1\nTj/9utlWfhZ4/1gaNq6RhFLKXaWUazbxeIA8H7RjRDy28/KjyA3+5SPUfR250Ee10yJvY/sz8rwK\npZTryQvZDu55+UHADeNZli016L4APkhe0f2YzgPgTeSQ46SYAv3QjiBcQF6s+LypdBRZSlkHLGT4\nMkTz93+M8LL/7JZvPKOZPlqZo3vKTBl97Aci4u3kUPIxPde8TEl96ourgcPIC5nb7cF3gIub32+a\noOZPmD6uEz8Bem8XPxi4dYoGhH72xTbkxeFdGzr1j6lx/bpS83vAT4E/BY4gTwmc1lPmauD5nb/f\nDtxFXnhyGHm72xKG3wL5JvIWpxcB84H3ASuB/fq1LFO1LyrzmbJ3N/SrH4DtyauCf07eArl75zFV\n7m44HljF8Fub7gIe1jz/QeD/dMo/EriPPL9+MPA6YC3w9E6ZJ5K3PLa3QL6HvH1qKt8C2Y9+OLlZ\n7hf2vPfbDnp5J7svKvN4MNzd0I914uHkiOInyFvkn00ebPzToJd3AH3x7qYvXtKUP5rcfp4x5nb1\ncYF3BE4nb0daBnwO2KanzHrgb3qmvYccLVhFDh8fUKn77eTIwX3k7T5PHPQbPKi+qNQxlUPChPcD\n8BfNa7qPDc3PfQa9zJ12vo78t+j3k0n/cZ3nvghc3FP+KeSRxf3Nh/pllTpfRIaq+4ErySPpgS/r\nZPYDcF3l/V8PvGvQyzqIdaKn/JQPCf3qB4ZGG1c1ZU6m+a/HU/nRh8/HNOCd5HfSrGzq/gQwb6xt\n8l9FS5Kkqil736gkSRosQ4IkSaoyJEiSpCpDgiRJqjIkSJKkKkOCJEmqMiRIkqQqQ4IkSaoyJEiS\npCpDgrQViYgvdv6F95qIWBIR72z+I2db5jURcVlE3BcRyyLiioh4U0TMbZ5/VER8IyKua+p64+CW\nSFI/GRKkrc+5wB7kf8r7MPlPYN4KEBGnAx8BvgU8lfwPgu8Dnkf+cxjI/yy3lPw+/FuR9JA1Y9AN\nkDTp1pRS7mh+//eIOA54fkRcB/w1+U/CzumUvxE4u/mX3JRSfkr+N08i4kOT2G5Jk8yRBEmrgVnA\nCcDVPQHhD0op901qqyQNnCFB2opFxNOBY4CLgQOB3wy2RZKmEk83SFuf50bEfcBMIICvAO8BnjvI\nRkmaegwJ0tbnYuC1wDrgllLKBoCIuAY4ZJANkzS1eLpB2vqsLKVcV0r5XRsQGmcAB0VEdUQhIuZN\nTvMkTRWGBEkAlFK+BnwNODMi/jkiFkTEPhHxnIj4PnlLJBExMyIeExF/Ql7wuHfz9/zBtV5SP0Qp\nZdBtkDRJIuKLwA6llONGKfMa4JXAHwEPAEuAs4CPl1JWR8S+wHVA78bjR6WUI/vTckmDYEiQJElV\nnm6QJElVhgRJklRlSJAkSVWGBEmSVGVIkCRJVYYESZJUZUiQJElVhgRJklRlSJAkSVWGBEmSVGVI\nkCRJVYYESZJU9f8BCgDS9ffIYT0AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11062db38>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(X_kpca[y==0, 0], np.zeros((500, 1)), \n",
    "            color='red', marker='o', alpha=0.5)\n",
    "plt.scatter(X_kpca[y==1, 0], np.zeros((500, 1)), \n",
    "            color='blue', marker='^', alpha=0.5)\n",
    "\n",
    "plt.title('First principal component after RBF Kernel PCA')\n",
    "plt.xlabel('PC1')\n",
    "plt.yticks([])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## API"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "## RBFKernelPCA\n",
      "\n",
      "*RBFKernelPCA(gamma=15.0, n_components=None, copy_X=True)*\n",
      "\n",
      "RBF Kernel Principal Component Analysis for dimensionality reduction.\n",
      "\n",
      "**Parameters**\n",
      "\n",
      "- `gamma` : float (default: 15.0)\n",
      "\n",
      "    Free parameter (coefficient) of the RBF kernel.\n",
      "\n",
      "- `n_components` : int (default: None)\n",
      "\n",
      "    The number of principal components for transformation.\n",
      "    Keeps the original dimensions of the dataset if `None`.\n",
      "\n",
      "- `copy_X` : bool (default: True)\n",
      "\n",
      "    Copies training data, which is required to compute the projection\n",
      "    of new data via the transform method. Uses a reference to X if False.\n",
      "\n",
      "**Attributes**\n",
      "\n",
      "- `e_vals_` : array-like, shape=[n_features]\n",
      "\n",
      "    Eigenvalues in sorted order.\n",
      "\n",
      "- `e_vecs_` : array-like, shape=[n_features]\n",
      "\n",
      "    Eigenvectors in sorted order.\n",
      "\n",
      "- `X_projected_` : array-like, shape=[n_samples, n_components]\n",
      "\n",
      "    Training samples projected along the component axes.\n",
      "\n",
      "### Methods\n",
      "\n",
      "<hr>\n",
      "\n",
      "*fit(X)*\n",
      "\n",
      "Learn model from training data.\n",
      "\n",
      "**Parameters**\n",
      "\n",
      "- `X` : {array-like, sparse matrix}, shape = [n_samples, n_features]\n",
      "\n",
      "    Training vectors, where n_samples is the number of samples and\n",
      "    n_features is the number of features.\n",
      "\n",
      "**Returns**\n",
      "\n",
      "- `self` : object\n",
      "\n",
      "\n",
      "<hr>\n",
      "\n",
      "*transform(X)*\n",
      "\n",
      "Apply the non-linear transformation on X.\n",
      "\n",
      "**Parameters**\n",
      "\n",
      "- `X` : {array-like, sparse matrix}, shape = [n_samples, n_features]\n",
      "\n",
      "    Training vectors, where n_samples is the number of samples and\n",
      "    n_features is the number of features.\n",
      "\n",
      "**Returns**\n",
      "\n",
      "- `X_projected` : np.ndarray, shape = [n_samples, n_components]\n",
      "\n",
      "    Projected training vectors.\n",
      "\n",
      "\n"
     ]
    }
   ],
   "source": [
    "with open('../../api_modules/mlxtend.feature_extraction/RBFKernelPCA.md', 'r') as f:\n",
    "    s = f.read()\n",
    "print(s)"
   ]
  }
 ],
 "metadata": {
  "anaconda-cloud": {},
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.5.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}
